PROPER CLARKE EPIDERIVATIVE IN SET-VALUED OPTIMIZATION

被引：1

作者：

Lalitha, C. S. ^{[2
]}

Arora, R. ^{[1
]}

机构：

[1] Univ Delhi, Dept Math, Delhi 110007, India

[2] Univ Delhi S Campus, Dept Math, New Delhi 110021, India

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2009年 / 13卷 / 6A期

关键词：

Set-valued optimization; Epiderivative; Proper minimizers; Tangent cone; Semilocal convexity; OPTIMALITY CONDITIONS; CONTINGENT EPIDERIVATIVES; EFFICIENT SOLUTIONS;

D O I：

10.11650/twjm/1500405609

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the concept of Clarke tangent cone, a new notion of proper Clarke epiderivative for a set-valued map is introduced. Its nature and certain properties are investigated. Finally necessary and sufficient optimality conditions for a constrained set-valued optimization problem have been established in terms of proper Clarke epiderivative.

引用

页码：1695 / 1710

页数：16

共 24 条

[1] [Anonymous], 1981, MATH ANAL APPL
[2] Bao TQ, 2007, CONTROL CYBERN, V36, P531
[3] K-epiderivatives for set-valued functions and optimization
Bigi, G
Castellani, M
[J]. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2002, 55 (03) : 401 - 412
[4] Optimality conditions for set-valued optimization problems
Chen, GY
Jahn, J
[J]. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 1998, 48 (02) : 187 - 200
[5] CHEN L, 2002, J NONLINEAR CONVEX A, V3, P303
[6] OPTIMALITY CONDITIONS FOR MAXIMIZATIONS OF SET-VALUED FUNCTIONS
CORLEY, HW
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1988, 58 (01) : 1 - 10
[7] SUFFICIENT CONDITIONS FOR GLOBAL MINIMA OF SUITABLY CONVEX FUNCTIONALS FROM VARIATIONAL AND CONTROL-THEORY
EWING, GM
[J]. SIAM REVIEW, 1977, 19 (02) : 202 - 220
[8] Optimality conditions for Henig and globally proper efficient solutions with ordering cone has, empty interior
Gong, XH
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 307 (01) : 12 - 31
[9] Optimality conditions for proper efficient solutions of vector set-valued optimization
Gong, XH
Dong, HB
Wang, SY
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 284 (01) : 332 - 350
[10] Gopfert A., 2003, Variational Methods in Partially Ordered Spaces

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