{"title":"Solving Unconstrained Optimization Problems with Some Three-term Conjugate Gradient Methods","authors":"Ladan Arman","doi":"10.5556/j.tkjm.54.2023.4185","DOIUrl":null,"url":null,"abstract":"In this paper, based on the efficient Conjugate Descent ({\\tt CD}) method, two generalized {\\tt CD}algorithms are proposed to solve the unconstrained optimization problems.These methods are three-term conjugate gradient methods which the generateddirections by using the conjugate gradient parameters and independent of the line searchsatisfy in the sufficient descent condition. Furthermore, under the strong Wolfe line search,the global convergence of the proposed methods are proved. Also, the preliminary numericalresults on the {\\tt CUTEst} collection are presented to show effectiveness of our methods.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/j.tkjm.54.2023.4185","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, based on the efficient Conjugate Descent ({\tt CD}) method, two generalized {\tt CD}algorithms are proposed to solve the unconstrained optimization problems.These methods are three-term conjugate gradient methods which the generateddirections by using the conjugate gradient parameters and independent of the line searchsatisfy in the sufficient descent condition. Furthermore, under the strong Wolfe line search,the global convergence of the proposed methods are proved. Also, the preliminary numericalresults on the {\tt CUTEst} collection are presented to show effectiveness of our methods.
期刊介绍:
To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.