On solving generalized Nash equilibrium problems via optimization
- 252 Downloads
This paper deals with the generalized Nash equilibrium problem (GNEP), i.e. a noncooperative game in which the strategy set of each player, as well as his payoff function, depends on the strategies of all players. We consider an equivalent optimization reformulation of GNEP using a regularized Nikaido–Isoda function so that solutions of GNEP coincide with global minima of the optimization problem. We then propose a derivative-free descent type method with inexact line search to solve the equivalent optimization problem and we prove that our algorithm is globally convergent. The convergence analysis is not based on conditions guaranteeing that every stationary point of the optimization problem is a solution of GNEP. Finally, we present the performance of our algorithm on some examples.
KeywordsGeneralized Nash equilibrium problem Nikaido–Isoda function Descent method
Unable to display preview. Download preview PDF.
- 2.Auslender A.: Optimization. Méthodes Numériques. Masson, Paris (1976)Google Scholar
- 8.Panicucci, B., Pappalardo, M., Passacantando, M.: A globally convergent descent method for nonsmooth variational inequalities. Comput. Optim. Appl. (2007). doi: 10.1007/s10589-007-9132-y
- 11.von Heusinger, A., Kanzow, C.: Optimization reformulations of the generalized Nash equilibrium problem using Nikaido–Isoda-type functions. Comput. Optim. Appl. (2007). doi: 10.1007/s10589-007-9145-6
- 12.von Heusinger, A., Kanzow, C.: Relaxation methods for generalized Nash equilibrium problem with inexact line search. Preprint 282, Institute of Mathematics, University of Würzburg, Würzburg, February (2008)Google Scholar