Generalized Nash Equilibrium Problems of Polynomials

We consider generalized Nash equilibrium problems (GNEPs) given by polynomial functions. Based on the Karush-Kuhn-Tucker optimality conditions, we formulate polynomial optimization problems for finding candidate solutions to GNEPs, using Lagrange multiplier expressions. Then, for nonconvex GNEPs, we introduce the feasible extensions to preclude KKT points that are not solutions to the GNEP. Following this sequel, we are able to find a GNE if there exists any, or detect the nonexistence of GNEs. We showed that our approach guarantees to solve the GNEP within finitely many steps under generic assumptions.