An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints

Abstract

Generalized Nash Equilibrium Problems (GNEP) have been attracted by many researchers in the field of game theory, operational research, engineering, economics as well as telecommunication in recent two decades. One of the most important classes of GNEP is a convex GNEP with jointly convex or shared constraints which has been studied extensively. It is considered to be one of the most challenging classes of problems in the field. Moreover, there is a gap in the studies on the GNEP with coupling and shared constraints. The aim of this paper is to investigate the relationship between an exact penalty approach and conjugate duality in convex optimization for the GNEP with coupling and shared constraints. In association with necessary optimality conditions, we obtained the parameterized variational inequality problems. This problem has provided an opportunity to solve many other GNEs. Some numerical results are also presented.

Keywords

• generalized nash equilibrium problems
• exact penalty function
• conjugate duality
• coupling and shared constraints