A parallel splitting method for weakly coupled monotone inclusions

TL;DR

This paper introduces a flexible parallel splitting method for solving complex systems of coupled monotone inclusions, capable of handling multiple variables and nonlinear couplings, with broad applications across various scientific fields.

Contribution

It presents a novel parallel algorithm that extends classical methods to multiple variables and nonlinear couplings, with proven convergence.

Findings

Convergence established for diverse coupling schemes

Applicable to evolution inclusions and dynamical games

Effective in signal recovery and image decomposition

Abstract

A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two variables and linear coupling, our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes. The breadth and flexibility of the proposed framework is illustrated through applications in the areas of evolution inclusions, dynamical games, signal recovery, image decomposition, best approximation, network flows, and variational problems in Sobolev spaces.