Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality

doi:10.1007/s10957-016-1007-x

	Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality
	Grapiglia, Geovani Nunes 1; Yuan, Jinyun 1; Yuan, Ya-xiang2
	2016-12-01
发表期刊	JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN	0022-3239
卷号	171 期号:3 页码:980-997
摘要	A nonlinear stepsize control (NSC) framework has been proposed by Toint (Optim Methods Softw 28:82-95, 2013) for unconstrained optimization, generalizing several trust-region and regularization algorithms. More recently, worst-case complexity bounds to achieve approximate first-order optimality were proved by Grapiglia, Yuan and Yuan (Math Program 152:491-520, 2015) for the generic NSC framework. In this paper, improved complexity bounds for first-order optimality are obtained. Furthermore, complexity bounds for second-order optimality are also provided.
关键词	Worst-case complexity Trust-region methods Regularization methods Unconstrained optimization
DOI	10.1007/s10957-016-1007-x
语种	英语
资助项目	Coordination for Improvement of Higher Education Personnel (CAPES), Brazil ; Coordination of the Improvement of Higher Education Personnel (CAPES) ; National Council for Scientific and Technological Development (CNPq), Brazil ; Natural Science Foundation of China (NSFC), China
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000389232900012
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24338
专题	计算数学与科学工程计算研究所
通讯作者	Grapiglia, Geovani Nunes
作者单位	1.Univ Fed Parana, Dept Matemat, Ctr Politecn, Cx Postal 19-081, BR-81531980 Curitiba, Parana, Brazil 2.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn, Acad Math & Syst Sci, Zhong Guan Cun Donglu 55, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Grapiglia, Geovani Nunes,Yuan, Jinyun,Yuan, Ya-xiang. Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,2016,171(3):980-997.
APA	Grapiglia, Geovani Nunes,Yuan, Jinyun,&Yuan, Ya-xiang.(2016).Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,171(3),980-997.
MLA	Grapiglia, Geovani Nunes,et al."Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality".JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 171.3(2016):980-997.