A Douglas-Rachford Splitting Method for Solving Equilibrium Problems

Abstract

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.

12 pages

References in corpus (2)

• Weak convergence on Douglas-Rachford method
• Outer approximation method for constrained composite fixed point problems involving Lipschitz pseudo contractive operators

Cited by in corpus (4)

• Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping
• A Class of Randomized Primal-Dual Algorithms for Distributed Optimization
• A randomized intertial primal-dual fixed point algorithm for monotone inclusions
• Continuous time approximation of Nash equilibria