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STABILIZED BARZILAI-BORWEIN METHOD
Burdakov, Oleg1; Dai, Yuhong2; Huang, Na3
2019
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume37Issue:6Pages:916-936
AbstractThe Barzilai-Borwein (BB) method is a popular and efficient tool for solving large-scale unconstrained optimization problems. Its search direction is the same as for the steepest descent (Cauchy) method, but its stepsize rule is different. Owing to this, it converges much faster than the Cauchy method. A feature of the BB method is that it may generate too long steps, which throw the iterates too far away from the solution. Moreover, it may not converge, even when the objective function is strongly convex. In this paper, a stabilization technique is introduced. It consists in bounding the distance between each pair of successive iterates, which often allows for decreasing the number of BB iterations. When the BB method does not converge, our simple modification of this method makes it convergent. For strongly convex functions with Lipschits gradients, we prove its global convergence, despite the fact that no line search is involved, and only gradient values are used. Since the number of stabilization steps is proved to be finite, the stabilized version inherits the fast local convergence of the BB method. The presented results of extensive numerical experiments show that our stabilization technique often allows the BB method to solve problems in a fewer iterations, or even to solve problems where the latter fails.
KeywordUnconstrained optimization Spectral algorithms Stabilization Convergence analysis
DOI10.4208/jcm.1911-m2019-0171
Indexed BySCI
Language英语
Funding ProjectVisiting Scientist award under the Chinese Academy of Sciences President's International Fellowship Initiative ; Chinese Natural Science Foundation[11631013] ; National 973 Program of China[2015CB856002]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000504738100009
PublisherGLOBAL SCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50493
Collection中国科学院数学与系统科学研究院
Corresponding AuthorHuang, Na
Affiliation1.Linkoping Univ, Dept Math, Linkoping, Sweden
2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
3.China Agr Univ, Coll Sci, Dept Appl Math, Beijing 100083, Peoples R China
Recommended Citation
GB/T 7714
Burdakov, Oleg,Dai, Yuhong,Huang, Na. STABILIZED BARZILAI-BORWEIN METHOD[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2019,37(6):916-936.
APA Burdakov, Oleg,Dai, Yuhong,&Huang, Na.(2019).STABILIZED BARZILAI-BORWEIN METHOD.JOURNAL OF COMPUTATIONAL MATHEMATICS,37(6),916-936.
MLA Burdakov, Oleg,et al."STABILIZED BARZILAI-BORWEIN METHOD".JOURNAL OF COMPUTATIONAL MATHEMATICS 37.6(2019):916-936.
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