Department Colloquia: On numerical approaches to solve the generalized Nash equilibirum problem and their implementations in Julia

SPEAKER:  TANGI MIGOT

ABSTRACT:

The generalized Nash equilibrium problem (GNEP) is an N player game, where each player has to solve a non-linear optimization problem whose objective function and constraints depend on the solutions of the other players. The GNEP is becoming a very popular modeling tool with an increasing need for numerical methods with efficient implementation. In this talk, we present two numerical approaches to tackle the GNEP: a decomposition method and a method based on nonsmooth dynamical systems. These methods have been included in a Julia (https://julialang.org) framework to solve the GNEP. We finally present numerical results on a benchmark of games from the literature.