A parallel subgradient projection algorithm for quasiconvex equilibrium problems under the intersection of convex sets

TL;DR

This paper introduces a parallel projection algorithm for quasiconvex equilibrium problems constrained by intersecting convex sets, with proven convergence and demonstrated effectiveness through numerical examples.

Contribution

It proposes a novel parallel subgradient projection algorithm that handles quasiconvex equilibrium problems with intersection constraints, improving computational efficiency.

Findings

Algorithm converges under specified conditions.

Numerical examples validate the algorithm's effectiveness.

Applicable to variational inequalities with affine fractional operators.

Abstract

In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection-algorithm, where the projection can be computed independently onto each component set. The convergence of the algorithm is investigated and numerical examples for a variational inequality problem involving affine fractional operator are provided to demonstrate the behavior of the algorithm.