用三项共轭梯度法求解无约束优化问题

IF 0.7 Q2 MATHEMATICS

Tamkang Journal of Mathematics Pub Date : 2022-09-16 DOI:10.5556/j.tkjm.54.2023.4185

Ladan Arman

{"title":"用三项共轭梯度法求解无约束优化问题","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":"{\"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}","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

摘要

本文在高效共轭下降法({\tt CD})的基础上，提出了求解无约束优化问题的两种广义{\tt CD}算法。这些方法是利用共轭梯度参数生成方向的三项共轭梯度方法，不依赖于直线搜索，满足充分下降条件。在强Wolfe线搜索条件下，证明了所提方法的全局收敛性。此外，还给出了{\tt CUTEst}集合的初步数值结果，以显示我们的方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Solving Unconstrained Optimization Problems with Some Three-term Conjugate Gradient Methods

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Tamkang Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

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.