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Local saddle points for unconstrained polynomial optimization

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Abstract

This paper gives an algorithm for computing local saddle points for unconstrained polynomial optimization. It is based on optimality conditions and Lasserre’s hierarchy of semidefinite relaxations. It can determine the existence of local saddle points. When there are several different local saddle point values, the algorithm can get them from the smallest one to the largest one.

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Data sharing is not applicable to this article as no datasets are generated or analyzed during the study of this article.

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Acknowledgements

The authors would like to thank the editors and anonymous referees for the valuable advice. Wenjie Zhao was supported by Postgraduate Scientific Research Innovation Project of Hunan Province (CX20210605). Guangming Zhou was supported by Natural Science Foundation of China (12071399) and Key Projects of Hunan Provincial Education Department (18A048).

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  1. School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, 411105, Hunan, China

    Wenjie Zhao & Guangming Zhou

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  1. Wenjie Zhao
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  2. Guangming Zhou
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Correspondence to Guangming Zhou.

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Zhao, W., Zhou, G. Local saddle points for unconstrained polynomial optimization. Comput Optim Appl 82, 89–106 (2022). https://doi.org/10.1007/s10589-022-00361-3

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