English

The Saddle Point Problem of Polynomials

Optimization and Control 2021-06-10 v3

Abstract

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 number of Lasserre type semidefinite relaxations; ii) if there is no saddle point, our algorithm can detect its nonexistence.

Keywords

Cite

@article{arxiv.1809.01218,
  title  = {The Saddle Point Problem of Polynomials},
  author = {Jiawang Nie and Zi Yang and Guangming Zhou},
  journal= {arXiv preprint arXiv:1809.01218},
  year   = {2021}
}

Comments

23 pages

R2 v1 2026-06-23T03:54:20.732Z