Optimal High-Order Methods for Solving Monotone Variational Inequalities

arXiv:2609.23557 · math.OC, cs.GT, stat.ML · Submitted 2026-09-20 · Read on arXiv

math.OC, cs.GT, stat.ML

Submitted: 2026-09-20

Updated: 2026-09-20

Comments: Improve our previous note in https://arxiv.org/abs/2608.08463 and achieve optimal complexity

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Anchored Tensor Method — 7× in this paper
• Regularization — 7× in this paper · explained in 3 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Lyapunov function — 3× in this paper · explained in 2 episodes
• Newton Proximal Extragradient — 3× in this paper
• AUC — 2× in this paper · explained in 2 episodes
• Regret — 2× in this paper · explained in 3 episodes
• APEX — 1× in this paper · explained in 1 episode
• Accuracy — 1× in this paper · explained in 1 episode
• Adversarial Training — 1× in this paper · explained in 1 episode
• Closed-Loop Control — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• Optimal Methods for Higher-Order Smooth Monotone Variational Inequalities
• Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(\epsilon^{-4/(3p+1)})$ $p$th-Order Oracle Complexity
• Halpern Iteration Achieves (epsilon-1/p) p th-Order Oracle Complexity for Monotone Variational Inequalities
• High-Order Reduced-Gradient Methods for Composite Variational Inequalities

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