The cone condition and nonsmoothness in linear generalized Nash games

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.


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