Penalty methods for the solution of generalized Nash equilibrium problems. (English) Zbl 1211.90228

Facchinei, Francisco; Kanzow, Christian

SIAM J. Optim. 20, No. 5, 2228-2253 (2010).

Summary: The generalized Nash equilibrium problem (GNEP) is an extension of the classical Nash equilibrium problem where both the objective functions and the constraints of each player may depend on the rivals’ strategies. This class of problems has a multitude of important engineering applications, and yet solution algorithms are extremely scarce. In this paper, we analyze in detail a globally convergent penalty method that has favorable theoretical properties. We also consider strengthened results for a particular subclass of problems very often considered in the literature. Basically our method reduces the GNEP to a single penalized (and nonsmooth) Nash equilibrium problem. We suggest a suitable method for the solution of the latter penalized problem and present extensive numerical results.

MSC:

90C30	Nonlinear programming
91A10	Noncooperative games
65K05	Numerical mathematical programming methods

Keywords:

Nash equilibrium problem; generalized Nash equilibrium problem; jointly convex problem; exact penalty function; global convergence