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题名	A globally convergent proximal Newton-type method in nonsmooth convex optimization
作者	Mordukhovich，Boris S.1; Yuan，Xiaoming 2; Zeng，Shangzhi 3; Zhang，Jin4
通讯作者	Mordukhovich，Boris S.; Zhang，Jin
发表日期	2022
DOI	10.1007/s10107-022-01797-5
发表期刊	MATHEMATICAL PROGRAMMING 影响因子和分区
ISSN	0025-5610
EISSN	1436-4646
卷号	198 期号:1页码:899-936
摘要	The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of variational analysis, we establish implementable results on the global convergence of the proposed algorithm as well as its local convergence with superlinear and quadratic rates. For certain structured problems, the obtained local convergence conditions do not require the local Lipschitz continuity of the corresponding Hessian mappings that is a crucial assumption used in the literature to ensure a superlinear convergence of other algorithms of the proximal Newton type. The conducted numerical experiments of solving the l regularized logistic regression model illustrate the possibility of applying the proposed algorithm to deal with practically important problems.
关键词	Global and local convergence Machine learning Metric subregularity Nonsmooth convex optimization Proximal Newton methods
相关链接	[Scopus记录]
收录类别	SCI ; EI
语种	英语
学校署名	通讯
资助项目	USA National Science Foundation["DMS-1512846","DMS-1808978"] ; USA Air Force Office of Scientific Research[15RT04] ; Australian Research Council[DP-190100555] ; Hong Kong Research Grants Council[12302318] ; National Science Foundation of China[11971220] ; Shenzhen Science and Technology Program[RCYX20200714114700072] ; Stable Support Plan Program of Shenzhen Natural Science Fund[20200925152128002]
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:000771841900001
出版者	SPRINGER HEIDELBERG
EI入藏号	20221311845743
EI主题词	Convex optimization ; Machine learning ; Regression analysis ; Variational techniques
EI分类号	Calculus:921.2 ; Numerical Methods:921.6 ; Mathematical Statistics:922.2
ESI学科分类	COMPUTER SCIENCE
Scopus记录号	2-s2.0-85126901514
来源库	Scopus
引用统计	被引频次[WOS]：13
成果类型	期刊论文
条目标识符	//www.snoollab.com/handle/2SGJ60CL/327808
专题	理学院_数学系深圳国家应用数学中心
作者单位	1.Department of Mathematics,Wayne State University,Detroit,MI,United States 2.Department of Mathematics,The University of Hong Kong,Hong Kong 3.Department of Mathematics and Statistics,University of Victoria,Victoria,Canada 4.Department of Mathematics,Southern University of Science and Technology,National Center for Applied Mathematics Shenzhen,Shenzhen,518055,China
通讯作者单位	数学系; 深圳国家应用数学中心
推荐引用方式 GB/T 7714	Mordukhovich，Boris S.,Yuan，Xiaoming,Zeng，Shangzhi,et al. A globally convergent proximal Newton-type method in nonsmooth convex optimization[J]. MATHEMATICAL PROGRAMMING,2022,198(1):899-936.
APA	Mordukhovich，Boris S.,Yuan，Xiaoming,Zeng，Shangzhi,&Zhang，Jin.(2022).A globally convergent proximal Newton-type method in nonsmooth convex optimization.MATHEMATICAL PROGRAMMING,198(1),899-936.
MLA	Mordukhovich，Boris S.,et al."A globally convergent proximal Newton-type method in nonsmooth convex optimization".MATHEMATICAL PROGRAMMING 198.1(2022):899-936.