Finite Convergence and Sharp Minima for Quasi-Equilibrium Problems

The notion of sharp minima, given by Polyak, is an important tool in studying the convergence analysis of algorithms designed to solve optimization problems. It has been studied extensively for variational inequality problems and equilibrium problems. In this paper, the convergence analysis of the sequence generated by proximal point method for quasi-equilibrium problem (QEP) will be established under sharp minima conditions. Further, the characterizations of weak sharp solution for QEP are provided. We also introduce an inexact proximal point method and demonstrate the convergence of the sequence for solving the QEP. Finally, we deduce the proximal point approximation for generalized Nash equilibrium problem.