Distributed Fast Fixed-Point Algorithms for Composite Monotone Inclusions over Networks

This paper aims to develop new and efficient distributed algorithms for solving a class of monotone inclusions, 0 in sum i=1 n (G ix + T ix), over a connected network of n agents, where the single-valued operator G i and the possibly multivalued operator T i remain private to agent i. Existing distributed algorithms for this problem class are primarily non-accelerated, and their exact convergence rates in the original primal space are largely unexplored. To bridge this gap, we propose two Decentralized Fast Fixed-Point-based algorithms, ND-DFFP and NI-DFFP, which integrate Nesterov-type acceleration with primal-dual techniques under two prominent settings: (i) Lipschitz continuity of G i and maximal monotonicity of G i+T i; and (ii) co-coercivity of G i and maximal monotonicity of T i. While ND-DFFP utilizes a homogeneous network-dependent stepsize, NI-DFFP reformulates the problem into a three-operator inclusion to decouple the network topology, enabling heterogeneous network-independent stepsizes. Under appropriate assumptions, we establish an O(1/k) convergence rate for the consensus error and an O(1/k) rate for both the restricted gap function and the squared forward-backward splitting residual, with the latter two metrics evaluated at the network-average iterate or its projection onto the effective domain. Finally, numerical experiments on distributed bilinear matrix games and a virtual power plant problem demonstrate the competitive performance and computational efficiency of our methods over recent decentralized baselines in the literature.