Distributed forward-backward methods for ring networks

In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion in the product space. Each iteration of the studied algorithms requires one resolvent evaluation per set-valued operator, one forward evaluation per cocoercive operator, and two forward evaluations per monotone operator. Unlike existing methods, the structure of the proposed algorithms are suitable for distributed, decentralised implementation in ring networks without needing global summation to enforce consensus between nodes.Funding Agencies|CRUE-CSIC agreement; Springer Nature; Ministry of Science, Innovation and Universities of Spain; European Regional Development Fund (ERDF) of the European Commission [PGC2018097960-B-C22]; Generalitat Valenciana [AICO/2021/165]; Wallenberg Al, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation [305286]; Australian Research Council [DE200100063]; MINECO; European Social Fund [PRE2019-090751]</p