Parallel extragradient-proximal methods for split equilibrium problems

TL;DR

This paper introduces two parallel extragradient-proximal algorithms for efficiently solving split equilibrium problems, combining multiple optimization techniques and establishing convergence under common assumptions.

Contribution

The paper presents novel parallel extragradient-proximal methods that integrate extragradient, proximal, and hybrid approaches for split equilibrium problems, with proven convergence.

Findings

Algorithms converge weakly and strongly under standard assumptions

Methods effectively combine multiple optimization techniques

Theoretical convergence guarantees are established

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 hybrid (outer approximation) method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions.