A POLYNOMIAL OPTIMIZATION FRAMEWORK FOR POLYNOMIAL QUASI-VARIATIONAL INEQUALITIES WITH MOMENT-SOS RELAXATIONS

被引：0

作者：

Tang, Xindong ^{[1
,2
]}

Zhang, Min ^{[3
]}

Zhong, Wenzhi ^{[2
,4
]}

机构：

[1] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Kowloon, Hong Kong, Peoples R China

[2] Hong Kong Baptist Univ, Inst Res & Continuing Educ, Shenzhen, Peoples R China

[3] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China

[4] Univ Bath, Dept Math Sci, Bath, England

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2024年

基金：

中国国家自然科学基金;

关键词：

Quasi-variational inequality; polynomial optimization; Lagrange multiplier expression; Moment-SOS hierarchy; DUAL GAP FUNCTION; CONVEXITY;

D O I：

10.3934/naco.2024054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider quasi-variational inequality problems (QVI) given by polynomial functions. By applying Lagrange multiplier expressions, we formulate polynomial optimization problems whose minimizers are KKT points for the QVI. Then, feasible extensions are exploited to preclude KKT points that are not solutions. Moment-SOS relaxations are incorporated to solve the polynomial optimization problems in our methods. Under certain conditions, our approach guarantees to find a solution to the QVI or detect the nonexistence of solutions.

引用

页数：23

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