An Inexact Penalty Method for Non Stationary Generalized Variational Inequalities

Abstract

We consider a set-valued (generalized) variational inequality problem in a finite-dimensional setting, where only approximation sequences are known instead of exact values of the cost mapping and feasible set. We suggest to apply a sequence of inexact solutions of auxiliary problems involving general penalty functions. Its convergence is attained without concordance of penalty, accuracy, and approximation parameters under certain coercivity type conditions.