无约束优化多步曲线搜索法的收敛性

J. Num. Math. Pub Date : 2004-11-01 DOI:10.1515/1569395042571292

Zhenjun Shi

{"title":"无约束优化多步曲线搜索法的收敛性","authors":"Zhenjun Shi","doi":"10.1515/1569395042571292","DOIUrl":null,"url":null,"abstract":"A new multi-step curve search method for unconstrained minimization problems is proposed. The convergence of the algorithm is proved under some mild conditions. The linear convergence rate is also investigated when the objective function is uniformly convex. This method uses previous multi-step iterative information and curve search rule to generate new iterative points. Using more previous iterative information and curve search rule can make the new method converge more stably than traditional descent methods and be suitable to solve large scale problems.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"15 4","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":"{\"title\":\"Convergence of multi-step curve search method for unconstrained optimization\",\"authors\":\"Zhenjun Shi\",\"doi\":\"10.1515/1569395042571292\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new multi-step curve search method for unconstrained minimization problems is proposed. The convergence of the algorithm is proved under some mild conditions. The linear convergence rate is also investigated when the objective function is uniformly convex. This method uses previous multi-step iterative information and curve search rule to generate new iterative points. Using more previous iterative information and curve search rule can make the new method converge more stably than traditional descent methods and be suitable to solve large scale problems.\",\"PeriodicalId\":342521,\"journal\":{\"name\":\"J. Num. Math.\",\"volume\":\"15 4\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"J. Num. Math.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/1569395042571292\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Num. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/1569395042571292","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 13

摘要

针对无约束最小化问题，提出了一种新的多步曲线搜索方法。在较温和的条件下证明了算法的收敛性。研究了目标函数为一致凸时的线性收敛速度。该方法利用先前的多步迭代信息和曲线搜索规则生成新的迭代点。该方法使用了更多的先验迭代信息和曲线搜索规则，比传统的下降法收敛更稳定，适用于求解大规模问题。

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

Convergence of multi-step curve search method for unconstrained optimization

A new multi-step curve search method for unconstrained minimization problems is proposed. The convergence of the algorithm is proved under some mild conditions. The linear convergence rate is also investigated when the objective function is uniformly convex. This method uses previous multi-step iterative information and curve search rule to generate new iterative points. Using more previous iterative information and curve search rule can make the new method converge more stably than traditional descent methods and be suitable to solve large scale problems.

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

J. Num. Math.

自引率

0.00%

发文量