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

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