On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization

doi:10.1007/s10107-014-0794-9

	On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization
	Grapiglia, Geovani N.1,2; Yuan, Jinyun 1,3; Yuan, Ya-xiang
	2015-08-01
发表期刊	MATHEMATICAL PROGRAMMING
ISSN	0025-5610
卷号	152 期号:1-2 页码:491-520
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.
关键词	Global convergence Worst-case complexity Trust-region methods Regularization methods Unconstrained Optimization Composite nonsmooth optimization Multiobjective optimization
DOI	10.1007/s10107-014-0794-9
语种	英语
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
WOS类目	Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000358292600016
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20405
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.