About Hahn-Banach extension theorems and applications to set-valued optimization

被引：1

作者：

Hernandez, Elvira ^{[1
]}

Rodriguez-Marin, Luis ^{[1
]}

Sama, Miguel ^{[1
]}

机构：

[1] Univ Nacl Educ Distancia, Dept Matemat Aplicada, ETSI Ind, E-28040 Madrid, Spain

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2012年 / 64卷 / 06期

关键词：

Hahn-Banach theorem; Set-valued map; Affine selection; Set optimization; Lagrange multiplier theorem; Affinelike map; VECTOR OPTIMIZATION; MAPS; MULTIFUNCTIONS; EFFICIENCY;

D O I：

10.1016/j.camwa.2012.02.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we revise several generalizations of the algebraic Hanh-Banach extension theorem for set-valued maps and give new versions in terms of set-relations and selections. We apply our results by establishing optimality conditions for a set-valued constrained optimization problem considering several types of solutions. Finally, we give necessary conditions for the existence of affine selections via affinelike maps in the framework of linear spaces. (c) 2012 Elsevier Ltd. All rights reserved.

引用

页码：1778 / 1788

页数：11

共 50 条

[21] On some extension theorems for set-valued mappings
Zalinescu, C.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 88 : 24 - 26
[22] ON HAHN-BANACH TYPE EXTENSION THEOREM
ISEKI, K
KASAHARA, S
PROCEEDINGS OF THE JAPAN ACADEMY, 1965, 41 (01): : 29 - &
[23] LINEAR HAHN-BANACH EXTENSION OPERATORS
SIMS, B
YOST, D
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1989, 32 : 53 - 57
[24] Existence Theorems for Set-valued Operators in Banach Spaces
Shin-ya Matsushita
Wataru Takahashi
Set-Valued Analysis, 2007, 15 : 251 - 264
[25] The Convergence Theorems of Set-Valued Pramart in a Banach Space
Guan, Li
Li, Shoumei
NONLINEAR MATHEMATICS FOR UNCERTAINTY AND ITS APPLICATIONS, 2011, 100 : 135 - 142
[26] Existence theorems for set-valued operators in Banach spaces
Matsushita, Shin-ya
Takahashi, Wataru
SET-VALUED ANALYSIS, 2007, 15 (03): : 251 - 264
[27] Amenability of representations and invariant Hahn-Banach theorems
Junghenn, H. D.
JOURNAL OF ANALYSIS, 2020, 28 (04): : 931 - 949
[28] HAHN-BANACH TYPE THEOREMS FOR ADJOINT SEMIGROUPS
VANNEERVEN, JMAM
MATHEMATISCHE ANNALEN, 1990, 287 (01) : 63 - 71
[29] Hahn-Banach theorems for MV-algebras
Leustean, Ioana
SOFT COMPUTING, 2012, 16 (11) : 1845 - 1850
[30] HAHN-BANACH TYPE THEOREMS FOR HYPOLINEAR FUNCTIONALS
ANGER, B
LEMBCKE, J
MATHEMATISCHE ANNALEN, 1974, 209 (02) : 127 - 151

← 1 2 3 4 5 →