Extragradient methods for nonsmooth equilibrium problems in Banach spaces
Alfredo Noel Iusem, Vahid Mohebbi · Optimization · 2018
We introduce and analyse the extragradient method for solving nonsmooth equilibrium problems in Banach spaces, which generalizes the extragradient method for variational inequalities. We prove weak convergence of the generated sequence to a solution of the equilibrium problem, under standard assumptions on the bifunction which defines the problem, akin to those required in the convergence analysis of the method, when applied to solving variational inequalities. Then, we propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the problem.