Distributed forward-backward methods for ring networks

Abstract In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum finitely many monotone operators, which are not based on reduction to two operator inclusion in product space. Each iteration studied requires one resolvent evaluation per set-valued operator, forward cocoercive evaluations operator. Unlike existing methods, structure proposed suitable distributed, decentralised implementation ring networks without needing global summation enforce consensus between nodes.