Optimality conditions in non-convex set-valued optimization

被引：35

作者：

Flores-Bazán, F ^{[1
]}

机构：

[1] Univ Concepcion, Fac Ciencias Fis & Matemat, Dept Ingn Matemat, Concepcion, Chile

来源：

MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2001年 / 53卷 / 03期

关键词：

non-convex set-valued optimization; weak Pareto minima; closed radial cone; epiderivatives; optimality conditions;

D O I：

10.1007/s001860100130

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：

The notion of radial epiderivative is introduced and then a necessary and sufficient condition for a point to be a weak minimal solution (weak-efficient solution) for a non-convex set-valued optimization problem is derived. Such a condition subsumes various necessary and/or sufficient conditions found in the literature for single-valued convex/non-convex mappings.

引用

页码：403 / 417

页数：15

共 20 条

[1] On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems [J].

Amahroq, T ;

Thibault, L .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1995, 16 (9-10) :1293-1307

[2]

AUBIN JP, 1981, ADV MATH S, P160

[3]

AUBIN JP, 1996, SET VALUED ANAL

[4] DIRECTIONAL-DERIVATIVES IN NONSMOOTH OPTIMIZATION [J].

BENTAL, A ;

ZOWE, J .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1985, 47 (04) :483-490

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

Chen, GY ;

Jahn, J .

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

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

CORLEY, HW .

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

[7] Simplified optimality conditions for minimizing the difference of vector-valued functions [J].

Flores-Bazán, F ;

Oettli, W .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2001, 108 (03) :571-586

[8]

FLORESBAZAN F, 1999, 9926 U CONC DEP ING

[9]

Götz A, 2000, SIAM J OPTIMIZ, V10, P331

[10]

Hiriart-Urruty J. B., 1979, Mathematics of Operations Research, V4, P79, DOI 10.1287/moor.4.1.79

← 1 2 →