KMS Of Academy of mathematics and systems sciences, CAS
| On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization | |
Grapiglia, Geovani N.1,2; Yuan, Jinyun1,3; Yuan, Ya-xiang
| |
| 2015-08-01 | |
| Source Publication | MATHEMATICAL PROGRAMMING
 |
| ISSN | 0025-5610 |
| Volume | 152Issue:1-2Pages:491-520 |
| Abstract | A nonlinear stepsize control framework for unconstrained optimization was recently proposed by Toint (Optim Methods Softw 28:82-95, 2013), providing a unified setting in which the global convergence can be proved for trust-region algorithms and regularization schemes. The original analysis assumes that the Hessians of the models are uniformly bounded. In this paper, the global convergence of the nonlinear stepsize control algorithm is proved under the assumption that the norm of the Hessians can grow by a constant amount at each iteration. The worst-case complexity is also investigated. The results obtained for unconstrained smooth optimization are extended to some algorithms for composite nonsmooth optimization and unconstrained multiobjective optimization as well. |
| Keyword | Global convergence Worst-case complexity Trust-region methods Regularization methods Unconstrained Optimization Composite nonsmooth optimization Multiobjective optimization |
| DOI | 10.1007/s10107-014-0794-9 |
| Language | 英语 |
| Funding Project | CAPES, Brazil[PGCI 12347/12-4] ; CNPq, Brazil ; NSFC, China[11331012] |
| WOS Research Area | Computer Science ; Operations Research & Management Science ; Mathematics |
| WOS Subject | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000358292600016 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/20405 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Grapiglia, Geovani N. |
| Affiliation | 1.Univ Fed Parana, Dept Mat, BR-81531980 Curitiba, Parana, Brazil 2.Minist Educ Brazil, Capes Fdn, BR-70040020 Brasilia, DF, Brazil 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Grapiglia, Geovani N.,Yuan, Jinyun,Yuan, Ya-xiang. On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization[J]. MATHEMATICAL PROGRAMMING,2015,152(1-2):491-520. |
| APA | Grapiglia, Geovani N.,Yuan, Jinyun,&Yuan, Ya-xiang.(2015).On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization.MATHEMATICAL PROGRAMMING,152(1-2),491-520. |
| MLA | Grapiglia, Geovani N.,et al."On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization".MATHEMATICAL PROGRAMMING 152.1-2(2015):491-520. |
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