从按比例总最小二乘法的角度看 Barzilai-Borwein 步长族

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Computational Optimization and Applications Pub Date : 2024-01-18 DOI:10.1007/s10589-023-00546-4

Shiru Li, Tao Zhang, Yong Xia

{"title":"从按比例总最小二乘法的角度看 Barzilai-Borwein 步长族","authors":"Shiru Li, Tao Zhang, Yong Xia","doi":"10.1007/s10589-023-00546-4","DOIUrl":null,"url":null,"abstract":"<p>The Barzilai-Borwein (BB) steplengths play great roles in practical gradient methods for solving unconstrained optimization problems. Motivated by the observation that the two well-known BB steplengths correspond to the ordinary and the data least squares, respectively, we introduce a novel family of BB steplengths from the viewpoint of scaled total least squares. Numerical experiments demonstrate that high performance can be received by a carefully-selected BB steplength in the new family.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":"20 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A family of Barzilai-Borwein steplengths from the viewpoint of scaled total least squares\",\"authors\":\"Shiru Li, Tao Zhang, Yong Xia\",\"doi\":\"10.1007/s10589-023-00546-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The Barzilai-Borwein (BB) steplengths play great roles in practical gradient methods for solving unconstrained optimization problems. Motivated by the observation that the two well-known BB steplengths correspond to the ordinary and the data least squares, respectively, we introduce a novel family of BB steplengths from the viewpoint of scaled total least squares. Numerical experiments demonstrate that high performance can be received by a carefully-selected BB steplength in the new family.</p>\",\"PeriodicalId\":55227,\"journal\":{\"name\":\"Computational Optimization and Applications\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-01-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Optimization and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10589-023-00546-4\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Optimization and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10589-023-00546-4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

Barzilai-Borwein（BB）步长在解决无约束优化问题的实际梯度方法中发挥着重要作用。观察到两种著名的 BB 步长分别对应于普通最小二乘法和数据最小二乘法，受此启发，我们从比例总最小二乘法的角度引入了一种新的 BB 步长系列。数值实验证明，在新系列中精心选择 BB 步长可以获得很高的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A family of Barzilai-Borwein steplengths from the viewpoint of scaled total least squares

查看原文本刊更多论文

A family of Barzilai-Borwein steplengths from the viewpoint of scaled total least squares

The Barzilai-Borwein (BB) steplengths play great roles in practical gradient methods for solving unconstrained optimization problems. Motivated by the observation that the two well-known BB steplengths correspond to the ordinary and the data least squares, respectively, we introduce a novel family of BB steplengths from the viewpoint of scaled total least squares. Numerical experiments demonstrate that high performance can be received by a carefully-selected BB steplength in the new family.

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 Optimization and Applications 数学-应用数学

CiteScore

3.70

自引率

9.10%

发文量

审稿时长

10 months

期刊介绍： Computational Optimization and Applications is a peer reviewed journal that is committed to timely publication of research and tutorial papers on the analysis and development of computational algorithms and modeling technology for optimization. Algorithms either for general classes of optimization problems or for more specific applied problems are of interest. Stochastic algorithms as well as deterministic algorithms will be considered. Papers that can provide both theoretical analysis, along with carefully designed computational experiments, are particularly welcome. Topics of interest include, but are not limited to the following: Large Scale Optimization, Unconstrained Optimization, Linear Programming, Quadratic Programming Complementarity Problems, and Variational Inequalities, Constrained Optimization, Nondifferentiable Optimization, Integer Programming, Combinatorial Optimization, Stochastic Optimization, Multiobjective Optimization, Network Optimization, Complexity Theory, Approximations and Error Analysis, Parametric Programming and Sensitivity Analysis, Parallel Computing, Distributed Computing, and Vector Processing, Software, Benchmarks, Numerical Experimentation and Comparisons, Modelling Languages and Systems for Optimization, Automatic Differentiation, Applications in Engineering, Finance, Optimal Control, Optimal Design, Operations Research, Transportation, Economics, Communications, Manufacturing, and Management Science.