A Douglas-Rachford Splitting Method for Solving Equilibrium Problems

Details A Douglas-Rachford Splitting Method for Solving Equilibrium Problems A Douglas-Rachford Splitting Method for Solving Equilibrium Problems

2011-10-07

arxiv.org/abs/1110.1670v1

Mathematics

Optimization and Control

12 pages

Scientific paper

We propose a splitting method for solving an equilibrium problem involving the sum of two bifunctions satisfying standard conditions. We prove that this problem is equivalent to find a zero of two appropriate maximally monotone operators. Our algorithm is a consequence of the Douglas--Rachford splitting applied to this auxiliary monotone inclusion. Connections between monotone inclusions and equilibrium problems are studied.

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