Convex generalized Nash equilibrium problems and polynomial optimization

Abstract This paper studies convex generalized Nash equilibrium problems that are given by polynomials. We use rational and parametric expressions for Lagrange multipliers to formulate efficient polynomial optimization computing equilibria (GNEs). The Moment-SOS hierarchy of semidefinite relaxations used solve the optimization. Under some general assumptions, we prove method can find a GNE if there exists one, or detect nonexistence GNEs. Numerical experiments presented show efficiency method.