The set of correlated equilibria is convex and contains all Nash equilibria as special cases. Thus, the social welfare-maximizing correlated equilibrium is amenable to convex analysis and offers social welfare that is at least as good as the game s best performing Nash equilibria.We employ robust semidefinite programming (SDP) for computing the social welfare-maximizing correlated equilibria in static polynomial games, giving rise to a dedicated sequential SDP algorithm, the first of this type that can cope with multivariate strategy sets. We apply this algorithm to a wireless communication problem, where two mutually-interfering transmitters and receivers maximize their channel capacities.