New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems

被引：40

作者：

Li, S. J. ^{[1
]}

Zhu, S. K. ^{[1
]}

Teo, K. L. ^{[2
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

[2] Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2012年 / 152卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Set-valued optimization; Generalized second-order composed contingent epiderivative; Optimality conditions; OPTIMALITY CONDITIONS; VECTOR OPTIMIZATION; TANGENT SETS; MAPS;

D O I：

10.1007/s10957-011-9915-2

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we introduce the concept of a generalized second-order composed contingent epiderivative for set-valued maps and discuss its relationship to the generalized second-order contingent epiderivative. We also investigate some of its properties. Then, by virtue of the generalized second-order composed contingent epiderivative, we establish a unified second-order sufficient and necessary optimality condition for set-valued optimization problems, which is a generalization of the corresponding results in the literature.

引用

页码：587 / 604

页数：18

共 18 条

[1]

Aubin J.P., 1990, SET VALUED ANAL, DOI 10.1007/978-0-8176-4848-0

[2]

Aubin J.P., 1994, Differential Inclusions

[3]

Aubin JP, 1981, Mathematical analysis and applications, P160

[4] On sufficient second order optimality conditions in multiobjective optimization [J].

Bigi, G .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2006, 63 (01) :77-85

[5]

Bonnans J.F., 2013, PERTURBATION ANAL OP

[6] Second order optimality conditions based on parabolic second order tangent sets [J].

Bonnans, JF ;

Cominetti, R ;

Shapiro, A .

SIAM JOURNAL ON OPTIMIZATION, 1999, 9 (02) :466-492

[7] Optimality conditions for set-valued optimization problems [J].

Chen, GY ;

Jahn, J .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 1998, 48 (02) :187-200

[8] OPTIMALITY CONDITIONS FOR MAXIMIZATIONS OF SET-VALUED FUNCTIONS [J].

CORLEY, HW .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1988, 58 (01) :1-10

[9]

Durea M., 2004, REND CIRC MAT PALERM, V53, P451, DOI DOI 10.1007/BF02875738

[10] Contingent epiderivatives and set-valued optimization [J].

Jahn, J ;

Rauh, R .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 1997, 46 (02) :193-211

← 1 2 →