On differentiability properties of player convex generalized Nash equilibrium problems

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

AMS Subject Classifications:

• 91A10
• 90C31

Acknowledgments

We thank the anonymous referees for their precise and substantial remarks which helped to significantly improve the paper. The third author wishes to thank Christian Reger and Frieder Scharr for fruitful discussions on topics of this paper.

Notes

This research was partially supported by the DFG (Deutsche Forschungsgemeinschaft) under grants KA 1296/18-1 und STE 772/13-1.

This research was partially supported by the DFG (Deutsche Forschungsgemeinschaft) under grants KA 1296/18-1 und STE 772/13-1.