Application of the penalty method to limit quasi-equilibrium problems

Abstract

© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. We solve a general quasi-equilibrium problem in a finite-dimensional setting, where only approximation sequences are used instead of exact values of the bi-function and feasible map. We suggest to utilize a sequence of solutions of auxiliary problems based on a penalty method. Its convergence is attained without concordance of penalty and approximation parameters under mild coercivity type conditions.