Convex Generalized Nash Equilibrium Problems and Polynomial Optimization

DOI10.1007/S10107-021-01739-7arXiv2101.06504MaRDI QIDQ6358419

Publication date: 16 January 2021

Abstract: 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.

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Noncooperative games (91A10) Polynomial optimization (90C23)

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