KMS Of Academy of mathematics and systems sciences, CAS
| Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization | |
| Huang, Yakui1,2; Liu, Hongwei1 | |
| 2016-12-01 | |
| Source Publication | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
 |
| ISSN | 0926-6003 |
| Volume | 65Issue:3Pages:671-698 |
| Abstract | We present a smoothing projected Barzilai-Borwein (SPBB) algorithm for solving a class of minimization problems on a closed convex set, where the objective function is nonsmooth nonconvex, perhaps even non-Lipschitz. At each iteration, the SPBB algorithm applies the projected gradient strategy that alternately uses the two Barzilai-Borwein stepsizes to the smooth approximation of the original problem. Nonmonotone scheme is adopted to ensure global convergence. Under mild conditions, we prove convergence of the SPBB algorithm to a scaled stationary point of the original problem. When the objective function is locally Lipschitz continuous, we consider a general constrained optimization problem and show that any accumulation point generated by the SPBB algorithm is a stationary point associated with the smoothing function used in the algorithm. Numerical experiments on - problems, image restoration problems, and stochastic linear complementarity problems show that the SPBB algorithm is promising. |
| Keyword | Smoothing projected Barzilai-Borwein algorithm Constrained non-Lipschitz optimization Nonsmooth nonconvex optimization Smoothing approximation l(2)-l(p) problem Image restoration Stochastic linear complementarity problem |
| DOI | 10.1007/s10589-016-9854-9 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China (NNSFC)[61072144] ; National Natural Science Foundation of China (NNSFC)[61179040] ; Fundamental Research Funds for the Central Universities[K50513100007] |
| WOS Research Area | Operations Research & Management Science ; Mathematics |
| WOS Subject | Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000387773500005 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/24116 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Huang, Yakui |
| Affiliation | 1.Xidian Univ, Sch Math & Stat, Xian 710126, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Huang, Yakui,Liu, Hongwei. Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2016,65(3):671-698. |
| APA | Huang, Yakui,&Liu, Hongwei.(2016).Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,65(3),671-698. |
| MLA | Huang, Yakui,et al."Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 65.3(2016):671-698. |
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