Convex generalized Nash equilibrium problems and polynomial optimization
研究由多项式定义的凸广义纳什均衡问题，利用拉格朗日乘子的有理和参数表达式构造高效多项式优化，通过矩-SOS半定松弛求解，并证明方法能判断均衡存在性。
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 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.