Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 20, Issue 5, Pages 2228-2253Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090749499
Keywords
Nash equilibrium problem; generalized Nash equilibrium problem; jointly convex problem; exact penalty function; global convergence
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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.
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