KMS Of Academy of mathematics and systems sciences, CAS
A family of spectral gradient methods for optimization | |
Dai, Yu-Hong1,2; Huang, Yakui3; Liu, Xin-Wei3 | |
2019-09-01 | |
发表期刊 | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS |
ISSN | 0926-6003 |
卷号 | 74期号:1页码:43-65 |
摘要 | We propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the long Barzilai-Borwein (BB) stepsize and the short BB stepsize. Each member of the family is shown to share certain quasi-Newton property in the sense of least squares. The family also includes some other gradient methods as its special cases. We prove that the family of methods is R-superlinearly convergent for two-dimensional strictly convex quadratics. Moreover, the family is R-linearly convergent in the any-dimensional case. Numerical results of the family with different settings are presented, which demonstrate that the proposed family is promising. |
关键词 | Unconstrained optimization Steepest descent method Spectral gradient method R-linear convergence R-superlinear convergence |
DOI | 10.1007/s10589-019-00107-8 |
语种 | 英语 |
资助项目 | National Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[11701137] ; National Natural Science Foundation of China[11671116] ; National 973 Program of China[2015CB856002] |
WOS研究方向 | Operations Research & Management Science ; Mathematics |
WOS类目 | Operations Research & Management Science ; Mathematics, Applied |
WOS记录号 | WOS:000476600200002 |
出版者 | SPRINGER |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/35309 |
专题 | 计算数学与科学工程计算研究所 |
通讯作者 | Huang, Yakui |
作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Math Sci, Beijing 100049, Peoples R China 3.Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China |
推荐引用方式 GB/T 7714 | Dai, Yu-Hong,Huang, Yakui,Liu, Xin-Wei. A family of spectral gradient methods for optimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2019,74(1):43-65. |
APA | Dai, Yu-Hong,Huang, Yakui,&Liu, Xin-Wei.(2019).A family of spectral gradient methods for optimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,74(1),43-65. |
MLA | Dai, Yu-Hong,et al."A family of spectral gradient methods for optimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 74.1(2019):43-65. |
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