KMS Of Academy of mathematics and systems sciences, CAS
| New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization | |
| Zhao, Ting1; Liu, Hongwei1; Liu, Zexian2,3 | |
| 2020-10-28 | |
| Source Publication | NUMERICAL ALGORITHMS
 |
| ISSN | 1017-1398 |
| Pages | 34 |
| Abstract | In this paper, two new subspace minimization conjugate gradient methods based on p-regularization models are proposed, where a special scaled norm in p-regularization model is analyzed. Different choices of special scaled norm lead to different solutions to the p-regularized subproblem. Based on the analyses of the solutions in a two-dimensional subspace, we derive new directions satisfying the sufficient descent condition. With a modified nonmonotone line search, we establish the global convergence of the proposed methods under mild assumptions. R-linear convergence of the proposed methods is also analyzed. Numerical results show that, for the CUTEr library, the proposed methods are superior to four conjugate gradient methods, which were proposed by Hager and Zhang (SIAM J. Optim. 16(1):170-192, 2005), Dai and Kou (SIAM J. Optim. 23(1):296-320, 2013), Liu and Liu (J. Optim. Theory. Appl. 180(3):879-906, 2019) and Li et al. (Comput. Appl. Math. 38(1):2019), respectively. |
| Keyword | Conjugate gradient method p-regularization model Subspace technique Nonmonotone line search Unconstrained optimization |
| DOI | 10.1007/s11075-020-01017-1 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Science Foundation of China[11901561] ; Guangxi Natural Science Foundation[2018GXNSFBA281180] ; China Postdoctoral Science Foundation[2019M660833] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000582812700002 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/52395 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Liu, Hongwei |
| Affiliation | 1.Xidian Univ, Sch Math & Stat, Xian 710126, Peoples R China 2.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, AMSS, Beijing 100190, Peoples R China 3.Guizhou Univ, Sch Math & Stat, Guiyang 550025, Peoples R China |
| Recommended Citation GB/T 7714 | Zhao, Ting,Liu, Hongwei,Liu, Zexian. New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization[J]. NUMERICAL ALGORITHMS,2020:34. |
| APA | Zhao, Ting,Liu, Hongwei,&Liu, Zexian.(2020).New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization.NUMERICAL ALGORITHMS,34. |
| MLA | Zhao, Ting,et al."New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization".NUMERICAL ALGORITHMS (2020):34. |
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