下降PRP共轭梯度法的全局收敛性

IF 2.5 3区数学 Q1 MATHEMATICS, APPLIED

Computational & Applied Mathematics Pub Date : 2012-01-01 DOI:10.1590/S1807-03022012000100004

Min Li, Heying Feng, Jianguo Liu

{"title":"下降PRP共轭梯度法的全局收敛性","authors":"Min Li, Heying Feng, Jianguo Liu","doi":"10.1590/S1807-03022012000100004","DOIUrl":null,"url":null,"abstract":"Recently, Yu and Guan proposed a modified PRP method (called DPRP method) which can generate sufficient descent directions for the objective function. They established the global convergence of the DPRP method based on the assumption that stepsize is bounded away from zero. In this paper, without the requirement of the positive lower bound of the stepsize, we prove that the DPRP method is globally convergent with a modified strong Wolfe line search. Moreover, we establish the global convergence of the DPRP method with a Armijo-type line search. The numerical results show that the proposed algorithms are efficient. Mathematical subject classification: Primary: 90C30; Secondary: 65K05.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"The global convergence of a descent PRP conjugate gradient method\",\"authors\":\"Min Li, Heying Feng, Jianguo Liu\",\"doi\":\"10.1590/S1807-03022012000100004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recently, Yu and Guan proposed a modified PRP method (called DPRP method) which can generate sufficient descent directions for the objective function. They established the global convergence of the DPRP method based on the assumption that stepsize is bounded away from zero. In this paper, without the requirement of the positive lower bound of the stepsize, we prove that the DPRP method is globally convergent with a modified strong Wolfe line search. Moreover, we establish the global convergence of the DPRP method with a Armijo-type line search. The numerical results show that the proposed algorithms are efficient. Mathematical subject classification: Primary: 90C30; Secondary: 65K05.\",\"PeriodicalId\":50649,\"journal\":{\"name\":\"Computational & Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2012-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational & Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1590/S1807-03022012000100004\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational & Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1590/S1807-03022012000100004","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 5

摘要

最近，Yu和Guan提出了一种改进的PRP方法(称为DPRP方法)，该方法可以为目标函数生成足够的下降方向。他们基于步长有界远离零的假设，建立了DPRP方法的全局收敛性。本文在不要求步长为正下界的情况下，用改进的强Wolfe线搜索证明了DPRP方法是全局收敛的。此外，我们还利用armijo型线搜索建立了DPRP方法的全局收敛性。数值结果表明，该算法是有效的。数学学科分类:初级:90C30;二级:65 k05。

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

The global convergence of a descent PRP conjugate gradient method

Recently, Yu and Guan proposed a modified PRP method (called DPRP method) which can generate sufficient descent directions for the objective function. They established the global convergence of the DPRP method based on the assumption that stepsize is bounded away from zero. In this paper, without the requirement of the positive lower bound of the stepsize, we prove that the DPRP method is globally convergent with a modified strong Wolfe line search. Moreover, we establish the global convergence of the DPRP method with a Armijo-type line search. The numerical results show that the proposed algorithms are efficient. Mathematical subject classification: Primary: 90C30; Secondary: 65K05.

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

Computational & Applied Mathematics Mathematics-Computational Mathematics

CiteScore

4.50

自引率

11.50%

发文量

352

审稿时长

>12 weeks

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.