A Parallel Splitting Method for Coupled Monotone Inclusions

A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist. Unlike existing 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, variational problems, best approximation, and network flows. Key words. coupled systems, demiregular operator, evolution inclusion, forward-backward algorithm, maximal monotone operator, operator splitting, parallel algorithm, weak convergence AMS subject classifications. 47H05, 34G25, 65K10, 90C25, 90B20 DOI. 10.1137/090754297

• Type: Journal
• Year: 2010
• Where: SIAMCO
• Authors: Hedy Attouch, Luis M. Briceño-Arias, Patrick L. Combettes
• Keywords: Evolution Inclusion, Maximal Monotone Operator, Parallel Splitting Method, SIAMCO 2010