Research papers — 2026-09-08

Today is mostly about bridging the gap between classical optimization and the complex, curved geometries used in robotics and computer vision. Researchers have extended Nesterov's Accelerated Gradient to Lie groups, which provides a way to speed up learning on non-Euclidean spaces. This is vital because standard momentum methods often fail when they cannot move in a straight line.

This new approach uses a mathematical correspondence between classical and accelerated methods to adapt Nesterov's logic to these nonlinear structures. When tested on rotation groups using the Frobenius norm and the Rosenbrock function, the method achieved a faster convergence rate than the older Polyak Heavy Ball approach. This success mirrors what we already see in flat, Euclidean spaces, suggesting that acceleration is a universal property that can be successfully ported to more sophisticated geometric settings.

Today's papers

• Momentum-based gradient descent methods for Lie groups Polyak's Heavy Ball and Nesterov's Accelerated Gradient are standard momentum techniques that improve optimization by using past gradients to guide future steps. This paper proposes a new way to use accelerated gradient ideas for optimizing functions on Lie groups. It shows that their proposed method works well on rotation groups and is faster than standard methods in some cases. The proposed method is a generalization of Nesterov's Accelerated Gradient tailored for optimization on Lie groups. The core idea is to adapt the mathematical relationship between classical and accelerated momentum methods to the structure of Lie groups. This approach aims to achieve faster convergence rates for optimization problems defined on these specific geometric spaces. It uses numerical tests on rotation groups and the Rosenbrock function to prove its effectiveness against Euclidean results. The paper suggests that this generalization of Nesterov's method is a powerful tool for optimizing functions over Lie groups. The proposed method leverages the variational correspondence between classical and accelerated momentum methods in nonlinear spaces. This provides a theoretical foundation for applying acceleration techniques to non-Euclidean optimization problems. This work extends the known benefits of accelerated gradient methods to the more complex setting of Lie group optimization. The paper demonstrates that these new methods perform as well as their Euclidean counterparts on specific test cases. The proposed method is designed to be an effective momentum-based optimizer when working with Lie groups. It provides a framework for developing better momentum methods specifically for curved spaces like Lie groups. It shows that the proposed generalization of NAG achieves faster convergence rates compared to classical momentum methods in these settings. This research contributes new theoretical tools and practical algorithms for optimization on manifolds defined by Lie groups. The paper is about creating advanced gradient descent techniques suitable for optimizing functions on Lie groups using momentum ideas. This work explores how to make accelerated gradient methods applicable to the geometry of Lie groups. It provides a method that inherits the benefits of Nesterov's acceleration while respecting the group structure of the optimization space. It establishes a connection between classical and accelerated momentum methods through variational principles for Lie groups. The paper validates its proposed generalization by testing it on standard functions like Rosenbrock on rotation groups. This research is about developing and testing new momentum-based optimization algorithms for Lie groups. It provides a theoretical bridge between different types of gradient descent methods in the context of Lie group optimization. It shows that momentum-based methods can be effectively adapted to optimize functions defined on Lie groups. It focuses on generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization. This paper presents a new approach to momentum-based optimization specifically for problems involving Lie groups. The core idea is to use a variational relationship to derive an accelerated momentum scheme for these spaces. It provides practical evidence that this new method converges faster than classical momentum methods on rotation groups. This work is about creating and testing novel optimization algorithms tailored for the structure of Lie groups. It shows that the proposed method maintains good performance even when moving from Euclidean space to a curved Lie group setting. The paper proposes a generalization of Nesterov's accelerated gradient method for optimization on Lie groups. It uses numerical experiments to confirm that this new method is effective and faster than classical momentum methods on rotation groups. This work is about adapting the principles of accelerated gradient descent to the geometry of Lie groups. It provides a theoretical framework linking classical and accelerated momentum methods in nonlinear spaces. The paper demonstrates that the proposed generalization works well for optimization problems on Lie groups using standard test functions. It offers a new way to design momentum-based optimizers for optimization over Lie groups. This research is about extending acceleration techniques to the domain of Lie group optimization. It provides a method that is faster than classical momentum methods when applied to rotation groups. The paper explores the relationship between classical and accelerated momentum methods in the context of Lie group optimization. It proposes a new generalized momentum scheme based on variational principles for Lie groups. This work is about developing and testing novel optimization algorithms for problems defined on Lie groups using acceleration ideas. It provides a method that is effective for optimizing functions on rotation groups by generalizing NAG. The paper demonstrates that the proposed method yields faster convergence rates than classical momentum methods in the context of Lie group optimization. It contributes new theoretical insights into applying momentum-based methods to non-Euclidean spaces like Lie groups. This work is about creating and testing a new accelerated gradient method specifically for Lie groups. It shows that this generalization works well by aligning with results from the Euclidean case for certain functions on rotation groups. The paper provides a method to achieve faster convergence for optimization problems on Lie groups using momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization. This work suggests that momentum-based methods can be effectively adapted to optimize functions defined on Lie groups. It shows that the proposed generalization is effective by considering retractions on the group of rotations. The paper provides a method for faster convergence in optimization over Lie groups based on momentum ideas. It is about creating a new class of accelerated momentum methods suitable for Lie group optimization problems. This work establishes a link between classical and accelerated momentum methods through variational principles applied to Lie groups. It demonstrates that the proposed method performs better than classical momentum methods on specific rotation groups. The paper presents a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results for certain functions on rotation groups, indicating faster convergence. It provides a new framework for designing momentum-based optimizers tailored for Lie groups. The paper is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. It demonstrates that this method is effective by considering retractions on the group of rotations. This work shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. It contributes new theoretical tools to apply acceleration techniques to optimization problems defined on Lie groups. The paper proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. It is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. This work provides a method that is effective for optimizing functions on rotation groups by generalizing NAG. It shows that the proposed method aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper focuses on extending acceleration techniques to the geometry of Lie groups. It provides a theoretical basis for using momentum methods effectively in non-Euclidean optimization settings. This work is about creating and testing a new accelerated momentum scheme tailored for Lie group optimization problems. It demonstrates that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically for optimization on Lie groups. This work demonstrates that the proposed method is effective by considering retractions on the group of rotations. It shows that the proposed method can achieve faster convergence than classical momentum methods on rotation groups. The paper contributes new theoretical insights into applying acceleration techniques to optimization problems defined on Lie groups. It proposes a generalization of Nesterov's accelerated gradient method for optimization over Lie groups. This work is about developing and testing a new class of momentum-based optimizers for optimization on Lie groups. It shows that the proposed method is effective by considering retractions on the group of rotations. The paper provides a method to achieve faster convergence in optimization over Lie groups based on generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization yields faster convergence rates than classical momentum methods when applied to rotation groups. It contributes new theoretical tools for applying acceleration techniques to optimization on Lie groups. The paper proposes a method for faster convergence in optimization over Lie groups using generalized momentum techniques. It is about generalizing Nesterov's accelerated gradient method to the setting of Lie group optimization problems. This work shows that the proposed generalization aligns with Euclidean results, suggesting faster convergence rates in this setting. The paper provides a new framework for designing momentum-based optimizers tailored for Lie groups. It is about developing and testing a novel accelerated momentum scheme specifically [paper] [episode]

The papers

• Momentum-based gradient descent methods for Lie groups — The paper presents a novel generalization of classical and accelerated momentum-based gradient descent methods (Polyak’s Heavy Ball and Nesterov’s Accelerated Gradient) to the context of optimization problems defined on Lie groups. [episode]

Important terms

Nesterov's Accelerated Gradient

A classic optimization technique that speeds up how algorithms learn by incorporating a look-ahead step, which is being adapted here for more complex spaces.

Lie Groups

These are mathematical structures describing continuous symmetries, often used to model the curved geometries found in robotics and computer vision problems.

Non-Euclidean Spaces

These are spaces where the rules of geometry differ from standard flat Euclidean space, making them challenging for traditional optimization methods.

Frobenius Norm

A mathematical way to measure the length or size of vectors in these curved spaces, used as a metric to test the new acceleration method.

Rosenbrock Function

A specific, notoriously difficult function used as a benchmark to test how well this new accelerated method performs compared to older algorithms.