A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES 被引量：3

A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES

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摘要 This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.

作者 CHENGLIXIN TENGYANMEI

机构地区 DepartmentofMathematics DepartmentofMathematics

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2003年第3期395-402,共8页 数学年刊（B辑英文版）

基金 Project supported by the National Natural Science Foundation of China(No.10071063)

关键词 OPTIMIZATION Geometry of infinite dimensions Convexification of nonconvex function Convex function DIFFERENTIABILITY Locally convex space 强优化定理局部凸空间凸集凸函数 Frechet可微 Radon-Nikodym性质强暴露性 Minkowski空间

分类号 O177.39 [理学—基础数学] O174.13 [理学—基础数学]

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参考文献8

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8Stegall, C., Optimization of functions on certain subsets of Banach spaces, Math. Ann., 236(1978),171-176.

同被引文献4

1吴从,程立新.Differentiability of Convex Functions in Locally Convex Spaces（Ⅰ）──Continuous Convex Functions and Gateaux Differentiability[J].Journal of Harbin Institute of Technology(New Series),1994,1(1):7-12. 被引量：3
2CHENG LIXIN,TENG YANMEI.DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES[J].Chinese Annals of Mathematics,Series B,2005,26(4):611-632. 被引量：3
3程立新.局部凸空间中的可微性定理和扰动优化或变分原理(英文)[J].应用泛函分析学报,1999,1(3):231-244. 被引量：5
4程立新.Banach空间的p-Asplund伴随空间(英文)[J].应用泛函分析学报,2001,3(2):120-128. 被引量：5

引证文献3

1叶洪波.Fréchet空间的d一致可微性[J].数学研究,2005,38(4):378-382. 被引量：1
2Li Xing CHENG Xiao Yan LIU Mai Fang ZUO.A Linear Perturbed Palais-Smale Condition for Lower Semicontinuous Functions on Banach Spaces[J].Acta Mathematica Sinica,English Series,2008,24(11):1853-1860. 被引量：2
3滕岩梅.局部完备局部凸空间中的向量值变分原理[J].数学学报（中文版）,2013,56(6):957-960.

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1Fu Chun YANG,Zhou WEI,Dong WANG.Subdifferential Representation of Homogeneous Functions and Extension of Smoothness in Banach spaces[J].Acta Mathematica Sinica,English Series,2010,26(8):1535-1544. 被引量：1
2María D.ACOSTA,Jernimo ALAMINOS,Domingo GARCA,Manuel MAESTRE.A Variational Approach to Norm Attainment of Some Operators and Polynomials[J].Acta Mathematica Sinica,English Series,2010,26(12):2259-2268.
3钟延生.关于映射一致可微性的几个定理[J].山东理工大学学报（自然科学版）,2013,27(6):12-16.

1张宝娣,陈述涛,侍述军.Orlicz-Sobolev空间的强暴露性质[J].哈尔滨师范大学自然科学学报,2009,25(1):18-19.
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6Jean-Marie Emmanuel BERNARD.Density Results in Sobolev Spaces Whose Elements Vanish on a Part of the Boundary[J].Chinese Annals of Mathematics,Series B,2011,32(6):823-846.
7甄苓,经玲,林海波.两个泛函优化定理的证明[J].数学的实践与认识,2011,41(19):241-244.
8Song Wenhua(Dalian University of Technology, China).THE SIMULTANEOUS APPROXIMATION IN THE LOCALLY CONVEX SPACES[J].Analysis in Theory and Applications,1995,11(1):72-79.
9吴奖伦.GENERALIZED BOCHNER THEOREM ON LOCALLY CONVEX SPACES[J].Acta Mathematicae Applicatae Sinica,1997,13(1):57-63.
10KOSTIC Marko.Abstract Volterra equations in locally convex spaces[J].Science China Mathematics,2012,55(9):1797-1825. 被引量：2

Chinese Annals of Mathematics,Series B

2003年第3期

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A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES 被引量：3

参考文献8

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