Parallel Extragradient-Proximal Methods for Split Equilibrium Problems

Abstract

In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms.

Keywords

• equilibrium problem
• split equilibrium problem
• extragradient method
• proximal method
• parallel algorithm