Optimization Online


The cone condition and nonsmoothness in linear generalized Nash games

Oliver Stein (stein***at***kit.edu)
Nathan Sudermann-Merx (sudermann***at***kit.edu)

Abstract: We consider linear generalized Nash games and introduce the so-called cone condition which characterizes the smoothness of the Nikaido-Isoda function under weak assumptions. The latter mapping arises from a reformulation of the generalized Nash equilibrium problem as a possibly nonsmooth optimization problem. Other regularity conditions like LICQ or SMFC(Q) are only sufficient for smoothness, but have the advantage that they can be verified more easily than the cone condition. Therefore, we present special cases where these conditions are not only sufficient, but also necessary for smoothness of the Nikaido-Isoda function. Our main tool in the analysis is a global extension of the Nikaido-Isoda function that allows us to avoid technical issues that may appear at the boundary of the domain of the Nikaido-Isoda function.

Keywords: generalized Nash equilibrium problem; Nikaido-Isoda function; piecewise-linear function; genericity; parametric optimization; constraint qualification

Category 1: Other Topics (Game Theory )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Journal of Optimization Theory and Applications, 2015, DOI 10.1007/s10957-015-0779-8.


Entry Submitted: 03/26/2015
Entry Accepted: 03/26/2015
Entry Last Modified: 09/08/2015

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society