Scholarlink

<p>This paper studies the algebraic degree of generalized Nash equilibrium problems (GNEPs) given by polynomials. Their generalized Nash equilibria (GNEs), as well as their Karush-Kuhn-Tucker (KKT) or Fritz-John points, are algebraic functions in the coefficients of defining polynomials. We study the degrees of these algebraic functions, which also count the numbers of complex KKT or Fritz-John points. Under some genericity assumptions, we show that a GNEP has only finitely many complex Fritz-John points and every Fritz-John point is a KKT point. We also give formulae for algebraic degrees of GNEPs, which count the numbers of complex Fritz-John points for generic cases.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Algebraic degrees of generalized Nash equilibrium problems

  • 期刊论文

  • 发表日期：

    2025年2月21日

查看全文
  • Jiawang Nie,
  • Kristian Ranestad,
  • Xindong Tang

摘要

This paper studies the algebraic degree of generalized Nash equilibrium problems (GNEPs) given by polynomials. Their generalized Nash equilibria (GNEs), as well as their Karush-Kuhn-Tucker (KKT) or Fritz-John points, are algebraic functions in the coefficients of defining polynomials. We study the degrees of these algebraic functions, which also count the numbers of complex KKT or Fritz-John points. Under some genericity assumptions, we show that a GNEP has only finitely many complex Fritz-John points and every Fritz-John point is a KKT point. We also give formulae for algebraic degrees of GNEPs, which count the numbers of complex Fritz-John points for generic cases.