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On Differentiability Properties of Player Convex Generalized Nash Equilibrium Problems

Nadja Harms (nadja.harms***at***mathematik.uni-wuerzburg.de)
Christian Kanzow (kanzow***at***mathematik.uni-wuerzburg.de)
Oliver Stein (stein***at***kit.edu)

Abstract: This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem. By using several results from parametric optimization we show that, apart from exceptional cases, all locally minimal points of the reformulation are differentiability points of the objective function. This justifies a numerical approach which basically ignores the possible nondifferentiabilities.

Keywords: Generalized Nash equilibrium problem, player convexity, Nikaido-Isoda function, Gateaux differentiability, Frechet differentiability, parametric optimization

Category 1: Other Topics (Game Theory )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Optimization, DOI: 10.1080/02331934.2012.752822

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Entry Submitted: 03/22/2012
Entry Accepted: 03/23/2012
Entry Last Modified: 01/29/2013

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