{"title":"Improved randomized approaches to the location of a conservative hyperplane","authors":"Xiaosong Ding, Jun Ma, Xiuming Li, Xi Chen","doi":"10.1007/s11590-024-02136-7","DOIUrl":null,"url":null,"abstract":"<p>This paper presents improved approaches to the treatment of combinatorial challenges associated with the search process for conservative cuts arising in disjoint bilinear programming. We introduce a new randomized approach that leverages the active constraint information within a hyperplane containing the given local solution. It can restrict the search process to only one dimension and mitigate the impact of growing degeneracy imposed on computational loads. The utilization of recursion further refines our strategy by systematically reducing the number of adjacent vertices available for exchange. Extensive computational experiments validate that these approaches can significantly enhance computational efficiency to the scale of <span>\\(10^{-3}\\)</span> s, particularly for those problems with high dimensions and degrees of degeneracy.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-07-06","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/s11590-024-02136-7","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
Abstract
This paper presents improved approaches to the treatment of combinatorial challenges associated with the search process for conservative cuts arising in disjoint bilinear programming. We introduce a new randomized approach that leverages the active constraint information within a hyperplane containing the given local solution. It can restrict the search process to only one dimension and mitigate the impact of growing degeneracy imposed on computational loads. The utilization of recursion further refines our strategy by systematically reducing the number of adjacent vertices available for exchange. Extensive computational experiments validate that these approaches can significantly enhance computational efficiency to the scale of \(10^{-3}\) s, particularly for those problems with high dimensions and degrees of degeneracy.
本文提出了一种改进的方法，用于处理与不相邻双线性编程中出现的保守切分搜索过程相关的组合难题。我们引入了一种新的随机方法，该方法利用了包含给定局部解的超平面内的主动约束信息。它可以将搜索过程限制在一个维度内，并减轻不断增长的退化性对计算负荷的影响。利用递归进一步完善了我们的策略，系统地减少了可供交换的相邻顶点数量。广泛的计算实验验证了这些方法可以显著提高计算效率，达到 \(10^{-3}\) s 的规模，特别是对于那些具有高维度和退化度的问题。
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
