{"title":"A study of search directions in primal-dual interior-point methods for semidefinite programming","authors":"M. Todd","doi":"10.1080/10556789908805745","DOIUrl":null,"url":null,"abstract":"We discuss several different search directions which can be used in primal-dual interior-point methods for semidefinite programming problems and investigate their theoretical properties, including scale invariance, primal-dual symmetry, and whether they always generate well-defined directions. Among the directions satisfying all but at most two of these desirable properties are the Alizadeh-Haeberly-Overton, Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-HaralMonteiro, Nesterov-Todd, Gu, and Toh directions, as well as directions we will call the MTW and Half directions. The first five of these appear to be the best in our limited computational testing also.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"122","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/10556789908805745","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: 122
Abstract
We discuss several different search directions which can be used in primal-dual interior-point methods for semidefinite programming problems and investigate their theoretical properties, including scale invariance, primal-dual symmetry, and whether they always generate well-defined directions. Among the directions satisfying all but at most two of these desirable properties are the Alizadeh-Haeberly-Overton, Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-HaralMonteiro, Nesterov-Todd, Gu, and Toh directions, as well as directions we will call the MTW and Half directions. The first five of these appear to be the best in our limited computational testing also.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
