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On differentiability properties of player convex generalized Nash equilibrium problems
Abstract: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  Gâteaux differentiability  Fréchet differentiability  parametric optimization
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