A globalized Newton method for the computation of normalized Nash equilibria

The generalized Nash equilibrium is a Nash game, where not only the players’ cost functions, but also the constraints of a player depend on the rival players decisions. We present a globally convergent algorithm that is suited for the computation of a normalized Nash equilibrium in the generalized Nash game with jointly convex constraints. The main tool is the regularized Nikaido–Isoda function as a basis for a locally convergent nonsmooth Newton method and, in another way, for the definition of a merit function for globalization. We conclude with some numerical results.