The Multiplier-Penalty Method for Generalized Nash Equilibrium Problems in Banach Spaces
Christian Kanzow, Veronika Karl, Daniel J. Steck, Daniel Wachsmuth · SIAM Journal on Optimization · 2019
This paper deals with generalized Nash equilibrium problems (GNEPs) in Banach spaces. We give an existence result for normalized equilibria of jointly convex GNEPs and then propose an augmented Lagrangian-type algorithm for their computation. A thorough convergence analysis is conducted which considers the existence of subproblem solutions as well as the feasibility and optimality of limit points. We then apply our investigations to differential economic games and multiobjective optimal control problems governed by linear partial differential equations. Numerical results are provided to demonstrate the practical performance of the method.