On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization
文献类型：期刊论文
| 作者 | Grapiglia, Geovani N.1,2; Yuan, Jinyun1,3; Yuan, Ya-xiang
|
| 刊名 | MATHEMATICAL PROGRAMMING
 |
| 出版日期 | 2015-08-01 |
| 卷号 | 152期号:1-2页码:491-520 |
| 关键词 | Global convergence Worst-case complexity Trust-region methods Regularization methods Unconstrained Optimization Composite nonsmooth optimization Multiobjective optimization |
| ISSN号 | 0025-5610 |
| DOI | 10.1007/s10107-014-0794-9 |
| 英文摘要 | 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. |
| 资助项目 | CAPES, Brazil[PGCI 12347/12-4] ; CNPq, Brazil ; NSFC, China[11331012] |
| WOS研究方向 | Computer Science ; Operations Research & Management Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000358292600016 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/20404]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Grapiglia, Geovani N. |
| 作者单位 | 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 |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。