Characterizations of r-Convex Functions

doi:10.1007/s10957-009-9617-1

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	Characterizations of r-Convex Functions
	Zhao, Y. X.1; Wang, S. Y.1 ; Coladas Uria, L.2
	2010-04-01
发表期刊	JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN	0022-3239
卷号	145 期号:1 页码:186-195
摘要	This paper discusses some properties of r-convexity and its relations with some other types of convexity. A characterization of convex functions in terms of r-convexity is given without assuming differentiability. The concept of strict r-convexity is introduced. For a twice continuously differentiable function f, it is shown that the strict r-convexity of f is equivalent to a certain condition on a double dagger (2) f. Further, it is shown that this condition is satisfied by quasiconvex functions satisfying a less stringent condition.
关键词	Strict r-convexity r-convexity Positive-semidefinite matrices Positive-definite matrices Convex functions Quasiconvex functions
DOI	10.1007/s10957-009-9617-1
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000275754400011
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/10503
专题	系统科学研究所
通讯作者	Zhao, Y. X.
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China 2.Univ Santiago de Compostela, Fac Math, Dept Stat & Operat Res, Santiago De Compostela 15782, Spain
推荐引用方式 GB/T 7714	Zhao, Y. X.,Wang, S. Y.,Coladas Uria, L.. Characterizations of r-Convex Functions[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,2010,145(1):186-195.
APA	Zhao, Y. X.,Wang, S. Y.,&Coladas Uria, L..(2010).Characterizations of r-Convex Functions.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,145(1),186-195.
MLA	Zhao, Y. X.,et al."Characterizations of r-Convex Functions".JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 145.1(2010):186-195.