The Saddle Point Problem of Polynomials

被引：0
|
作者：
Jiawang Nie
Zi Yang
Guangming Zhou
机构：
[1] University of California San Diego,Department of Mathematics
[2] Xiangtan University,School of Mathematics and Computational Science
来源：
Foundations of Computational Mathematics | 2022年 / 22卷
关键词：
Saddle point; Polynomial; Nonsingularity; Lasserre relaxation; Semidefinite program; 90C22; 90C47; 49K35; 65K05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper studies the saddle point problem of polynomials. We give an algorithm for computing saddle points. It is based on solving Lasserre’s hierarchy of semidefinite relaxations. Under some genericity assumptions on defining polynomials, we show that: (i) if there exists a saddle point, our algorithm can get one by solving a finite hierarchy of Lasserre-type semidefinite relaxations; (ii) if there is no saddle point, our algorithm can detect its nonexistence.
引用
收藏
页码：1133 / 1169
页数：36
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