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Mathematics > Optimization and Control

arXiv:2208.03931 (math)
[Submitted on 8 Aug 2022 (v1), last revised 16 Feb 2023 (this version, v2)]

Title:On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials

Authors:Kisun Lee, Xindong Tang
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Abstract:The generalized Nash equilibrium problem (GNEP) is a kind of game to find strategies for a group of players such that each player's objective function is optimized. Solutions for GNEPs are called generalized Nash equilibria (GNEs). In this paper, we propose a numerical method for finding GNEs of GNEPs of polynomials based on the polyhedral homotopy continuation and the Moment-SOS hierarchy of semidefinite relaxations. We show that our method can find all GNEs if they exist, or detect the nonexistence of GNEs, under some genericity assumptions. Some numerical experiments are made to demonstrate the efficiency of our method.
Comments: 25 pages, Version to appear in Journal of Scientific Computing
Subjects: Optimization and Control (math.OC); Algebraic Geometry (math.AG)
MSC classes: 91A80, 91A06, 14Q05, 90C23
Cite as: arXiv:2208.03931 [math.OC]
  (or arXiv:2208.03931v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2208.03931

Submission history

From: Kisun Lee [view email]
[v1] Mon, 8 Aug 2022 06:17:33 UTC (27 KB)
[v2] Thu, 16 Feb 2023 09:58:54 UTC (29 KB)
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