Partial penalization for the solution of generalized Nash equilibrium problems

Authors:
Francisco Facchinei;Lorenzo Lampariello
Affiliations:
Department of Computer and System Sciences Antonio Ruberti, Sapienza University of Rome, Rome, Italy 00185;Department of Computer and System Sciences Antonio Ruberti, Sapienza University of Rome, Rome, Italy 00185
Venue:
Journal of Global Optimization
Year:
2011

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Abstract

In this paper we reformulate the generalized Nash equilibrium problem (GNEP) as a nonsmooth Nash equilibrium problem by means of a partial penalization of the difficult coupling constraints. We then propose a suitable method for the solution of the penalized problem and we study classes of GNEPs for which the penalty approach is guaranteed to converge to a solution. In particular, we are able to prove convergence for an interesting class of GNEPs for which convergence results were previously unknown.