Distributed Fast Fixed-Point Algorithms for Composite Monotone Inclusions over Networks
Abstract
This paper aims to develop new and efficient distributed algorithms for solving a class of monotone inclusions, 0 ∈ ∑i=1n (Gix + Tix), over a connected network of n agents, where the single-valued operator Gi and the possibly multivalued operator Ti 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, \texttt{ND-DFFP} and \texttt{NI-DFFP}, which integrate Nesterov-type acceleration with primal-dual techniques under two prominent settings: (i) \textit{Lipschitz continuity of Gi and maximal monotonicity of Gi+Ti}; and (ii) \textit{co-coercivity of Gi and maximal monotonicity of Ti}. While \texttt{ND-DFFP} utilizes a homogeneous network-dependent stepsize, \texttt{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.
Related
- Inexact Proximal Point and Tseng Algorithms with Nonsummable Errors to Solve Monotone Inclusions
- Accelerated Algorithms for Stochastic Monotone Inclusions with Fixed Queries
- Optimistic Gradient Algorithms with Randomized Coordinate and Variance Reduction Strategies for Composite Inclusions
- Weak and strong convergence of a general splitting approach for monotone multioperator inclusions
- Maximal Monotone Differential Inclusions with Volterra and One-Sided Lipschitz Perturbations under Nonlocal Initial Conditions and Applications
BibTeX
@misc{nguyentrung2026distributed,
title = {{Distributed Fast Fixed-Point Algorithms for Composite Monotone Inclusions over Networks}},
author = {Nghia Nguyen-Trung and Ion Necoara and Quoc Tran-Dinh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14953},
eprint = {2609.14953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14953},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Distributed Fast Fixed-Point Algorithms for Composite Monotone Inclusions over Networks
AU - Nghia Nguyen-Trung
AU - Ion Necoara
AU - Quoc Tran-Dinh
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.14953
UR - https://arxiv.org/abs/2609.14953
AB - This paper aims to develop new and efficient distributed algorithms for solving a class of monotone inclusions, 0 ∈ ∑_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, \texttt{ND-DFFP} and \texttt{NI-DFFP}, which integrate Nesterov-type acceleration with primal-dual techniques under two prominent settings: (i) \textit{Lipschitz continuity of G_i and maximal monotonicity of G_i+T_i}; and (ii) \textit{co-coercivity of G_i and maximal monotonicity of T_i}. While \texttt{ND-DFFP} utilizes a homogeneous network-dependent stepsize, \texttt{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.
ER -