STABILIZED BARZILAI-BORWEIN METHOD
文献类型：期刊论文
| 作者 | Burdakov, Oleg2; Dai, Yuhong3; Huang, Na1 |
| 刊名 | JOURNAL OF COMPUTATIONAL MATHEMATICS
 |
| 出版日期 | 2019 |
| 卷号 | 37期号:6页码:916-936 |
| 关键词 | Unconstrained optimization Spectral algorithms Stabilization Convergence analysis |
| ISSN号 | 0254-9409 |
| DOI | 10.4208/jcm.1911-m2019-0171 |
| 英文摘要 | The 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. |
| 资助项目 | Visiting 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研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000504738100009 |
| 出版者 | GLOBAL SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50492]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Huang, Na |
| 作者单位 | 1.China Agr Univ, Coll Sci, Dept Appl Math, Beijing 100083, Peoples R China 2.Linkoping Univ, Dept Math, Linkoping, Sweden 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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