Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems

被引：40

作者：

Gao, Y. ^{[1
]}

Hou, S. H. ^{[2
]}

Yang, X. M. ^{[1
]}

机构：

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

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

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2012年 / 152卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Vector optimization problems; Approximate solutions; epsilon-efficiency; Scalarization; Limiting subdifferentials; EKELANDS VARIATIONAL PRINCIPLE; EFFICIENCY;

D O I：

10.1007/s10957-011-9891-6

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, we introduce a new concept of I mu-efficiency for vector optimization problems. This extends and unifies various notions of approximate solutions in the literature. Some properties for this new class of approximate solutions are established, and several existence results, as well as nonlinear scalarizations, are obtained by means of the Ekeland's variational principle. Moreover, under the assumption of generalized subconvex functions, we derive the linear scalarization and the Lagrange multiplier rule for approximate solutions based on the scalarization in Asplund spaces.

引用

页码：97 / 120

页数：24

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