A Douglas-Rachford Splitting Method for Solving Equilibrium Problems
  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. 
Luis M. Brice\~no-Arias
math.OC