Descent and penalization techniques for equilibrium problems with nonlinear constraints

Abstract

This paper deals with equilibrium problems with nonlinear constraints. Exploiting a gap function recently introduced, which rely on a polyhedral approximation of the feasible region, we propose two descent methods. They are both based on the minimization of a suitable exact penalty function, but they use different rules for updating the penalization parameter and they rely on different types of line search. The convergence of both algorithms is proved under standard assumptions