A Barzilai-Borwein conjugate gradient method
文献类型：期刊论文
| 作者 | Dai YuHong1 ; Kou CaiXia2
|
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2016-08-01 |
| 卷号 | 59期号:8页码:1511-1524 |
| 关键词 | conjugate gradient method subspace minimization Barzilai-Bowein gradient method line search descent property global convergence |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-016-0279-2 |
| 英文摘要 | The linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient method, however, heavily restricted the use of conjugate gradient method for large-scale nonlinear optimization. This is, to the great extent, due to the requirement of a relatively exact line search at each iteration and the loss of conjugacy property of the search directions in various occasions. On the contrary, the limited-memory BFGS method and the Barzilai-Bowein gradient method share the so-called asymptotical one stepsize per line-search property, namely, the trial stepsize in the method will asymptotically be accepted by the line search when the iteration is close to the solution. This paper will focus on the analysis of the subspace minimization conjugate gradient method by Yuan and Stoer (1995). Specifically, if choosing the parameter in the method by combining the Barzilai-Borwein idea, we will be able to provide some efficient Barzilai-Borwein conjugate gradient (BBCG) methods. The initial numerical experiments show that one of the variants, BBCG3, is specially efficient among many others without line searches. This variant of the BBCG method might enjoy the asymptotical one stepsize per line-search property and become a strong candidate for large-scale nonlinear optimization. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000380212100005 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/23268]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Dai YuHong |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 2.Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China |
| 推荐引用方式 GB/T 7714 | Dai YuHong,Kou CaiXia. A Barzilai-Borwein conjugate gradient method[J]. SCIENCE CHINA-MATHEMATICS,2016,59(8):1511-1524. |
| APA | Dai YuHong,&Kou CaiXia.(2016).A Barzilai-Borwein conjugate gradient method.SCIENCE CHINA-MATHEMATICS,59(8),1511-1524. |
| MLA | Dai YuHong,et al."A Barzilai-Borwein conjugate gradient method".SCIENCE CHINA-MATHEMATICS 59.8(2016):1511-1524. |
入库方式： OAI收割
来源：数学与系统科学研究院
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