Abstract

The purpose of this paper is to introduce a strongly convergent algorithm for minimizingthe distance function under the solution set of a split equilibrium problem involvingpseudomonotone bifunctions. The proposed algorithm can be considered as a combination of the extragradient method for pseudomonotone equilibrium problems and a projectionprocedure for convex optimization. Under the commonly used assumptions inpseudomonotone equilibrium problems, the iterations generated by the algorithm are proved to converge strongly to the unique solution of the considered problem. We then apply the algorithm to a jointly constrained Nash equilibrium model. A simple numerical example is given to illustrate the proposed algorithm.