Rational Generalized Nash Equilibrium Problems
Rational Generalized Nash Equilibrium Problems
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DOI：
10.1137/21m1456285
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
Jiawang Nie;Xindong Tang;Suhan Zhong
中科院分区：
文献类型：
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作者：
Jiawang Nie;Xindong Tang;Suhan Zhong
本文研究由有理函数给出的广义纳什均衡问题。优化问题不假设为凸问题。引入拉格朗日乘子的有理表达式和KKT点的可行扩展来计算广义纳什均衡（GNE）。为了解决理性广义纳什均衡问题，我们给出了一个理性优化问题的层次。研究了可行扩展的存在性和计算方法。应用矩- sos松弛法求解合理优化问题。在一些一般假设下，我们证明了所提出的层次结构可以计算GNE，如果它存在或检测它的不存在。数值实验表明了该方法的有效性。
This paper studies generalized Nash equilibrium problems that are given by rational functions. The optimization problems are not assumed to be convex. Rational expressions for Lagrange multipliers and feasible extensions of KKT points are introduced to compute a generalized Nash equilibrium (GNE). We give a hierarchy of rational optimization problems to solve rational generalized Nash equilibrium problems. The existence and computation of feasible extensions are studied. The Moment-SOS relaxations are applied to solve the rational optimization problems. Under some general assumptions, we show that the proposed hierarchy can compute a GNE if it exists or detect its nonexistence. Numerical experiments are given to show the efficiency of the proposed method.