Second-order optimality conditions for set optimization using coradiant sets

被引：2

作者：

Yao, Bin ^{[1
,2
]}

Li, Shengjie ^{[1
]}

机构：

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

[2] Shihezi Univ, Coll Sci, Shihezi 832003, Peoples R China

来源：

OPTIMIZATION LETTERS | 2020年 / 14卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Second-order radial derivatives; Optimality conditions; Set optimization; Coradiant set; VALUED OPTIMIZATION; RADIAL EPIDERIVATIVES; ORDER RELATIONS; DERIVATIVES; SCALARIZATION; EFFICIENCY; MAPS;

D O I：

10.1007/s11590-019-01531-9

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 aim of this paper is to study second-order optimality conditions for a set-valued optimization problem with set criterion, where the order relation is induced by a set belong to a class of specific coradiant sets and is not necessarily a preorder. We introduce a notion of generalized second-order radial set, different from the classical second-order radial set, it is defined on a set, not on a point. Using the generalized second-order radial set, we introduce a new type of generalized second-order radial derivatives for set-valued maps and apply them to establish some necessary and sufficient conditions for the lower strict minimal solution of the set optimization problem.

引用

页码：2073 / 2086

页数：14

共 30 条

[1] Optimality conditions for set-valued maps with set optimization
Alonso, Maria
Rodriguez-Marin, Luis
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (09) : 3057 - 3064
[2] Ansari QH., 2012, Recent advances in vector optimization
[3] Aubin JP, 1982, MATH ANAL APPL A
[4] Bao TQ, 2010, ADV MATH ECON, V13, P113, DOI 10.1007/978-4-431-99490-9_5
[5] Chen GY, 2005, LECT NOTES ECON MATH, V541, P1, DOI 10.1007/3-540-28445-1
[6] EXISTENCE AND LAGRANGIAN-DUALITY FOR MAXIMIZATIONS OF SET-VALUED FUNCTIONS
CORLEY, HW
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1987, 54 (03) : 489 - 501
[7] Optimality Conditions for Set-Valued Optimisation Problems Using a Modified Demyanov Difference
Dempe, Stephan
Pilecka, Maria
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 171 (02) : 402 - 421
[8] Dhingra M., 2017, YUGOSL J OPER RES, V27, P153, DOI DOI 10.2298/YJOR170115011D
[9] Optimality conditions for a unified vector optimization problem with not necessarily preordering relations
Flores-Bazan, Fabian
Hernandez, Elvira
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2013, 56 (02) : 299 - 315
[10] STRICT EFFICIENCY IN SET-VALUED OPTIMIZATION
Flores-Bazan, Fabian
Jimenez, Bienvenido
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (02) : 881 - 908

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