SCALARIZATIONS AND LAGRANGE MULTIPLIERS FOR APPROXIMATE SOLUTIONS IN THE VECTOR OPTIMIZATION PROBLEMS WITH SET-VALUED MAPS

被引：9

作者：

Gao, Ying ^{[1
]}

Yang, Xinmin ^{[1
]}

Yang, Jin ^{[2
]}

Yan, Hong ^{[3
]}

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

[3] Hong Kong Polytech Univ, Dept Logist & Maritime Studies, Hong Kong, Hong Kong, Peoples R China

来源：

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION | 2015年 / 11卷 / 02期

基金：

美国国家科学基金会;

关键词：

Set-valued maps; vector optimization problems; approximate solutions; generalized subconvexlike; scalarizations; Lagrange multiplier theorems; EKELANDS VARIATIONAL PRINCIPLE; BENSON PROPER EFFICIENCY; OPTIMALITY CONDITIONS; SADDLE-POINTS; THEOREMS;

D O I：

10.3934/jimo.2015.11.673

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we characterize approximate solutions of vector optimization problems with set-valued maps. We gives several characterizations of generalized subconvexlike set-valued functions(see [10), which is a generalization of nearly subconvexlike functions introduced in [34]. We present alternative theorem and derived scalarization theorems for approximate solutions with generalized subconvexlike set-valued maps. And then, Lagrange multiplier theorems under generalized Slater constraint qualification are established.

引用

页码：673 / 683

页数：11

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