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arXiv · 1809.01218

The Saddle Point Problem of Polynomials

Jiawang Nie·Zi Yang·Guangming Zhou
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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.

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Jiawang Nie, Zi Yang, Guangming Zhou. 2018-09-04. The Saddle Point Problem of Polynomials. https://arxiv.org/abs/1809.01218

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