{"title":"Complexity analysis and numerical implementation of a new interior-point algorithm for semidefinite optimization","authors":"Billel Zaoui, Djamel Benterki, Samia Khelladi","doi":"10.1016/j.orl.2024.107192","DOIUrl":null,"url":null,"abstract":"<div><div>We generalize Zhang and Xu's (2011) <span><span>[22]</span></span> interior point algorithm for linear optimization to semidefinite optimization problems in order to define a new search direction. The symmetrization of the search direction is based on the full Nesterov-Todd scaling scheme. Moreover, we show that the obtained algorithm solves the studied problem in polynomial time and that the short-step algorithm has the best-known iteration bound, namely <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mi>log</mi><mo></mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>ε</mi></mrow></mfrac><mo>)</mo></math></span>-iterations. Finally, we report a comparative numerical study to show the efficiency of our proposed algorithm.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107192"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637724001287","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We generalize Zhang and Xu's (2011) [22] interior point algorithm for linear optimization to semidefinite optimization problems in order to define a new search direction. The symmetrization of the search direction is based on the full Nesterov-Todd scaling scheme. Moreover, we show that the obtained algorithm solves the studied problem in polynomial time and that the short-step algorithm has the best-known iteration bound, namely -iterations. Finally, we report a comparative numerical study to show the efficiency of our proposed algorithm.
期刊介绍：
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.
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