T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-02 DOI:10.1007/s10589-024-00582-8

Hiroki Marumo, Sunyoung Kim, Makoto Yamashita

引用次数: 0

Abstract

We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs was introduced by Zheng et al. (JGO 84:415–440, 2022). In this work, we propose a T-SDP relaxation for POPs with polynomial inequality constraints and show that the resulting T-SDP relaxation formulated with third-order tensors can be transformed into the standard SDP relaxation with block-diagonal structures. The convergence of the T-SDP relaxation to the optimal value of a given constrained POP is established under moderate assumptions as the relaxation level increases. Additionally, the feasibility and optimality of the T-SDP relaxation are discussed. Numerical results illustrate that the proposed T-SDP relaxation enhances numerical efficiency.

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用三阶张量对受约束多项式优化进行 T-半无限编程放松

我们研究受约束多项式优化问题（POPs）的T-半有限编程（SDP）松弛。Zheng 等（JGO 84:415-440, 2022）提出了针对无约束 POP 的 T-SDP 松弛法。在这项研究中，我们提出了一种针对多项式不等式约束的 POP 的 T-SDP 松弛，并证明了用三阶张量表述的 T-SDP 松弛可以转化为具有块对角结构的标准 SDP 松弛。随着松弛程度的增加，在适度假设条件下，T-SDP 松弛可以收敛到给定约束 POP 的最优值。此外，还讨论了 T-SDP 松弛的可行性和最优性。数值结果表明，建议的 T-SDP 松弛提高了数值效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.