Improved error bound and a hybrid method for generalized Nash equilibrium problems

Abstract

We exploit a recently proposed local error bound condition for a nonsmooth reformulation of the Karush---Kuhn---Tucker conditions of generalized Nash equilibrium problems (GNEPs) to weaken the theoretical convergence assumptions of a hybrid method for GNEPs that uses a smooth reformulation. Under the presented assumptions the hybrid method, which combines a potential reduction algorithm and an LP-Newton method, has global and fast local convergence properties. Furthermore we adapt the algorithm to a nonsmooth reformulation, prove under some additional strong assumptions similar convergence properties as for the smooth reformulation, and compare the two approaches.