分布式法卡斯定理和无差距对偶半有限程序的矩优化问题

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-04 DOI:10.1007/s11590-024-02097-x

Queenie Yingkun Huang, Vaithilingam Jeyakumar

{"title":"分布式法卡斯定理和无差距对偶半有限程序的矩优化问题","authors":"Queenie Yingkun Huang, Vaithilingam Jeyakumar","doi":"10.1007/s11590-024-02097-x","DOIUrl":null,"url":null,"abstract":"<p>We present a generalized Farkas’ Lemma for an inequality system involving distributions. This lemma establishes an equivalence between an infinite-dimensional system of moment inequalities and a semi-definite system, assuming that the support for the distributions is a spectrahedron. To the best of our knowledge, it is the first extension of Farkas’ Lemma to the distributional paradigm. Applying the new Lemma, we then establish no-gap duality results between a class of moment optimization problems and numerically tractable semi-definite programs.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A distributional Farkas’ lemma and moment optimization problems with no-gap dual semi-definite programs\",\"authors\":\"Queenie Yingkun Huang, Vaithilingam Jeyakumar\",\"doi\":\"10.1007/s11590-024-02097-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We present a generalized Farkas’ Lemma for an inequality system involving distributions. This lemma establishes an equivalence between an infinite-dimensional system of moment inequalities and a semi-definite system, assuming that the support for the distributions is a spectrahedron. To the best of our knowledge, it is the first extension of Farkas’ Lemma to the distributional paradigm. Applying the new Lemma, we then establish no-gap duality results between a class of moment optimization problems and numerically tractable semi-definite programs.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11590-024-02097-x\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11590-024-02097-x","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

我们提出了涉及分布不等式系统的广义法卡斯定理。假定分布的支持是一个谱面体，这个定理在无穷维矩不等式系统和半定式系统之间建立了等价关系。据我们所知，这是法尔卡斯定理在分布范式中的首次扩展。应用新的定理，我们在一类矩优化问题和数值可控的半有限程序之间建立了无差距对偶结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A distributional Farkas’ lemma and moment optimization problems with no-gap dual semi-definite programs

We present a generalized Farkas’ Lemma for an inequality system involving distributions. This lemma establishes an equivalence between an infinite-dimensional system of moment inequalities and a semi-definite system, assuming that the support for the distributions is a spectrahedron. To the best of our knowledge, it is the first extension of Farkas’ Lemma to the distributional paradigm. Applying the new Lemma, we then establish no-gap duality results between a class of moment optimization problems and numerically tractable semi-definite programs.

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

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.