On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials
Optimization and Control
2023-02-17 v2 Algebraic Geometry
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.
Cite
@article{arxiv.2208.03931,
title = {On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials},
author = {Kisun Lee and Xindong Tang},
journal= {arXiv preprint arXiv:2208.03931},
year = {2023}
}
Comments
25 pages, Version to appear in Journal of Scientific Computing