{"title":"A polynomial interior-point algorithm with improved iteration bounds for linear optimization","authors":"Liying Liu, Tao Hua","doi":"10.1007/s13160-023-00630-6","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we present a polynomial primal-dual interior-point algorithm for linear optimization based on a modified logarithmic barrier kernel function. Iteration bounds for the large-update interior-point method and the small-update interior-point method are derived. It is shown that the large-update interior-point method has the same polynomial complexity as the small-update interior-point method, which is the best known iteration bounds. Our result closes a long-existing gap in the theoretical complexity bounds for large-update interior-point method and small-update interior-point method.</p>","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"3 ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Japan Journal of Industrial and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13160-023-00630-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present a polynomial primal-dual interior-point algorithm for linear optimization based on a modified logarithmic barrier kernel function. Iteration bounds for the large-update interior-point method and the small-update interior-point method are derived. It is shown that the large-update interior-point method has the same polynomial complexity as the small-update interior-point method, which is the best known iteration bounds. Our result closes a long-existing gap in the theoretical complexity bounds for large-update interior-point method and small-update interior-point method.
期刊介绍：
Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.
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