The new extragradient method extended to equilibrium problems

Abstract

Malitsky and Semenov in (Cybern Syst Anal 50(2):271–277, 2014) introduced a new extragradient method for variational inequality problem. This paper extends the new extragradient method to equilibrium problems for pseudomonotone and Lipschitz-type continuous bifunctions. We have replaced naturally two projections in the new extragradient method by two optimization programs and proved the weak convergence of the proposed algorithm. The advantage of the algorithm is the computation of only one value of the bifunction in each iteration. In the numerical experiment, we see that the proposed algorithm has a competitive advantage over the time of execution and the iterative number.