Hybrid algorithms without the extra-steps for equilibrium problems

TL;DR

This paper presents new hybrid algorithms for solving systems of equilibrium problems that avoid costly extra-steps by using specially constructed cutting-halfspaces, ensuring strong convergence without complex feasible set procedures.

Contribution

The paper introduces hybrid algorithms that eliminate the need for extra-steps like extragradient and linesearch, simplifying computations for equilibrium problems.

Findings

Algorithms achieve strong convergence.

Avoidance of extra-steps reduces computational complexity.

Applicable to systems with complex feasible sets.

Abstract

In this paper, we introduce some new hybrid algorithms for finding a solution of a system of equilibrium problems. In these algorithms, by constructing specially cutting-halfspaces, we avoid using the extra-steps as in the extragradient method and the Armijo linesearch method which are inherently costly when the feasible set has a complex structure. The strong convergence of the algorithms is established.