A Multiplier-Penalty-Method for Generalized Nash Equilibrium Problems in Banach Spaces

Christian Kanzow, Veronika Karl, Daniel Steck, Daniel Wachsmuth

We consider the (jointly convex) generalized Nash equilibrium problem (GNEP) in a Banach space setting. In order to find a suitable solution, we modify some recent ideas from infinite-dimensional optimization problems and suggest to use a multiplier-penalty-type scheme in order to solve the underlying GNEP. Under some mild and problem-tailored assumptions, we discuss topics like the existence of solutions, the well-definedness of the algorithm, as well as the feasibility and optimality of accumulation points. Some numerical results illustrate the efficiency of the overall scheme.