New methods for solving nonconvex and singular generalized Nash equilibrium problems via polynomial optimization

The Generalized Nash Equilibrium Problem (GNEP) is a kind of game to find strategies for a group of players such that each player's objective function is optimized, given other players' strategies. The solution to the GNEP is called a Generalized Nash Equilibrium (GNE).
In this project, the PI will study nonconvex GNEPs given by polynomial functions. More specifically, we will investigate algorithms for finding GNEs of nonconvex GNEPs of polynomials efficiently. Also, we will develop numerical methods for solving large-scale GNEPs by exploiting sparsity. Besides that, we will study GNEs where the Karush-Kuhn-Tucker (KKT) conditions fail to hold and investigate new algorithms for finding GNEs when the GNEP has no GNE in the set of KKT points. In our approaches, polynomial optimization problems are formulated for finding GNEs of GNEPs of polynomials, and the moment-SOS hierarchy of semidefinite relaxations is applied to solve these polynomial optimization problems.