Optimality conditions for metrically consistent approximate solutions in vector optimization

被引：13

作者：

Gutierrez, C.

Jimenez, B.

Novo, V. ^{[1
]}

机构：

[1] Univ Nacl Educ Distancia, Dept Matemat Aplicada, E-28040 Madrid, Spain

[2] Univ Valladolid, Dept Matemat Aplicada, Valladolid, Spain

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2007年 / 133卷 / 01期

关键词：

vector optimization; epsilon-efficiency; scalarization; gauge functionals; generalized Chebyshev norms; CONVEX PARETO PROBLEMS; SADDLE-POINT THEOREMS; EPSILON-EFFICIENCY; VARIATIONAL-PRINCIPLES; SCALARIZATION; DUALITY; SETS;

D O I：

10.1007/s10957-007-9191-3

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, approximate solutions of vector optimization problems are analyzed via a metrically consistent epsilon-efficient concept. Several properties of the epsilon-efficient set are studied. By scalarization, necessary and sufficient conditions for approximate solutions of convex and nonconvex vector optimization problems are provided; a characterization is obtained via generalized Chebyshev norms, attaining the same precision in the vector problem as in the scalarization.

引用

页码：49 / 64

页数：16

共 30 条

[1]

[Anonymous], 2003, Variational Methods in Partially Ordered Spaces

[2]

[Anonymous], 1989, Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems

[3] New closedness results for efficient sets in multiple objective mathematical programming [J].