Iterative Methods for the Projected Solutions of Quasi-equilibrium Problems

TL;DR

This paper introduces two iterative algorithms for finding projected solutions to quasi-equilibrium problems, proves their convergence, and demonstrates their effectiveness through numerical experiments and an application to electricity market modeling.

Contribution

The paper develops and analyzes two new iterative methods for solving quasi-equilibrium problems with non-self constraint maps, extending existing solution techniques.

Findings

Algorithms converge under certain assumptions

Numerical experiments validate the methods' effectiveness

Application to electricity market model demonstrates practical utility

Abstract

Aussel et al. (J Optim Theory Appl 170 818-837 2016) introduced the concept of projected solutions for the quasi-variational inequalities with a non-self constraint map, that is, the case where the constraint map may take values outside the feasible set. This paper presents two iterative methods to determine the projected solutions for quasi-equilibrium problems (QEP). We prove the convergence of the sequence generated by iterative methods to a projected solution of the QEP under some suitable assumptions. Some encouraging numerical experiments are presented to show the performance of the proposed methods. As an application, we apply the proposed algorithms to solve an electricity market model.