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