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. © 2010 Society for Industrial and Applied Mathematics.

Penalty methods for the solution of generalized Nash equilibrium problems / Facchinei, Francisco; Christian, Kanzow. - In: SIAM JOURNAL ON OPTIMIZATION. - ISSN 1052-6234. - 20:5(2010), pp. 2228-2253. [10.1137/090749499]

Penalty methods for the solution of generalized Nash equilibrium problems

FACCHINEI, Francisco;
2010

Abstract

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. © 2010 Society for Industrial and Applied Mathematics.
2010
exact penalty function; generalized nash equilibrium problem; global convergence; jointly convex problem; nash equilibrium problem
01 Pubblicazione su rivista::01a Articolo in rivista
Penalty methods for the solution of generalized Nash equilibrium problems / Facchinei, Francisco; Christian, Kanzow. - In: SIAM JOURNAL ON OPTIMIZATION. - ISSN 1052-6234. - 20:5(2010), pp. 2228-2253. [10.1137/090749499]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/18312
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