用三阶张量对受约束多项式优化进行 T-半无限编程放松

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED Computational Optimization and Applications Pub Date : 2024-06-02 DOI:10.1007/s10589-024-00582-8

Hiroki Marumo, Sunyoung Kim, Makoto Yamashita

{"title":"用三阶张量对受约束多项式优化进行 T-半无限编程放松","authors":"Hiroki Marumo, Sunyoung Kim, Makoto Yamashita","doi":"10.1007/s10589-024-00582-8","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization\",\"authors\":\"Hiroki Marumo, Sunyoung Kim, Makoto Yamashita\",\"doi\":\"10.1007/s10589-024-00582-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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.</p>\",\"PeriodicalId\":55227,\"journal\":{\"name\":\"Computational Optimization and Applications\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-06-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Optimization and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10589-024-00582-8\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Optimization and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10589-024-00582-8","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

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。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

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

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Computational Optimization and Applications 数学-应用数学

CiteScore

3.70

自引率

9.10%

发文量

审稿时长

10 months

期刊介绍： Computational Optimization and Applications is a peer reviewed journal that is committed to timely publication of research and tutorial papers on the analysis and development of computational algorithms and modeling technology for optimization. Algorithms either for general classes of optimization problems or for more specific applied problems are of interest. Stochastic algorithms as well as deterministic algorithms will be considered. Papers that can provide both theoretical analysis, along with carefully designed computational experiments, are particularly welcome. Topics of interest include, but are not limited to the following: Large Scale Optimization, Unconstrained Optimization, Linear Programming, Quadratic Programming Complementarity Problems, and Variational Inequalities, Constrained Optimization, Nondifferentiable Optimization, Integer Programming, Combinatorial Optimization, Stochastic Optimization, Multiobjective Optimization, Network Optimization, Complexity Theory, Approximations and Error Analysis, Parametric Programming and Sensitivity Analysis, Parallel Computing, Distributed Computing, and Vector Processing, Software, Benchmarks, Numerical Experimentation and Comparisons, Modelling Languages and Systems for Optimization, Automatic Differentiation, Applications in Engineering, Finance, Optimal Control, Optimal Design, Operations Research, Transportation, Economics, Communications, Manufacturing, and Management Science.