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Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality
Grapiglia, Geovani Nunes1; Yuan, Jinyun1; Yuan, Ya-xiang2
2016-12-01
Source PublicationJOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN0022-3239
Volume171Issue:3Pages:980-997
AbstractA 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.
KeywordWorst-case complexity Trust-region methods Regularization methods Unconstrained optimization
DOI10.1007/s10957-016-1007-x
Language英语
Funding ProjectCoordination 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 Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000389232900012
PublisherSPRINGER/PLENUM PUBLISHERS
Citation statistics
Cited Times:9[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/24338
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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