A Penalty Approach for Generalized Nash Equilibrium Problem (Communications in Mathematical Research, 2021)
The generalized Nash equilibrium problem (GNEP) is a generalization ofthe standard Nash equilibrium problem (NEP), in which both the utility function andthe strategy space of each player depend on the strategies chosen by all other players.This problem has been used to model various problems in applications. However, theconvergent solution algorithms are extremely scare in the literature. In this paper,we present an incremental penalty method for the GNEP, and show that a solutionof the GNEP can be found by solving a sequence of smooth NEPs. We then applythe semismooth Newton method with Armijo line search to solve latter problems andprovide some results of numerical experiments to illustrate the proposed approach.
Keywords: Nash equilibrium problem; generalized Nash equilibrium problem; logarithmic barrier function; quasi-variational inequality; semismooth Newton method.