Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems

被引：8

作者：

Gao, Ying ^{[1
]}

Yang, Xinmin ^{[1
]}

Lee, Heung Wing Joseph ^{[2
]}

机构：

[1] Chongqing Normal Univ, Dept Math, Chongqing 400047, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2010年

基金：

美国国家科学基金会;

关键词：

VECTOR OPTIMIZATION; CONE CHARACTERIZATIONS; VARIATIONAL PRINCIPLE; EPSILON-EFFICIENCY; POINTS; PROPER;

D O I：

10.1155/2010/620928

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

We study first- and second-order necessary and sufficient optimality conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization problems. Here, tangent cone, is an element of-normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper (lower) directional derivatives are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.

引用

页数：17

共 28 条

[1]

Second-order optimality conditions in multiobjective optimization problems [J].

Aghezzaf, B ;

Hachimi, M .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1999, 102 (01) :37-50

[2]

The vector-valued variational principle in Banach spaces ordered by cones with nonempty interiors [J].

Bednarczuk, Ewa M. ;

Przybyla, Maciej J. .

SIAM JOURNAL ON OPTIMIZATION, 2007, 18 (03) :907-913

[3]

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

Bigi, G .

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

[4]

Bolintinéanu S, 2001, J CONVEX ANAL, V8, P71

[5]

PROPER EFFICIENT POINTS FOR MAXIMIZATIONS WITH RESPECT TO CONES [J].

BORWEIN, J .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1977, 15 (01) :57-63

[6]

CAMBINI A, 1997, 2 ORDER TANGENT SETS

[7]

Chen GY, 2005, LECT NOTES ECON MATH, V541, pVII

[8]

On approximate minima in vector optimization [J].

Dutta, J ;

Vetrivel, V .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2001, 22 (7-8) :845-859

[9]

Cone characterizations of approximate solutions in real vector optimization [J].

Engau, A. ;

Wiecek, M. M. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2007, 134 (03) :499-513

[10]

Gopfert A., 2003, Variational Methods in Partially Ordered Spaces

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