Duality in vector optimization via augmented Lagrangian

被引：4

作者：

Huy, N. Q. ^{[2
]}

Kim, D. S. ^{[1
]}

机构：

[1] Pukyong Natl Univ, Dept Appl Math, Pusan 608737, South Korea

[2] Hanoi Pedag Univ, Dept Math, Phuc Yen, Vinh Phuc Provi, Vietnam

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 386卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Vector optimization; Augmented Lagrangian duality; Penalty representation; R-+(m)-lower semicontinuity; R-+(m)-lower Lipschitz; SET-VALUED OPTIMIZATION; CONJUGATE DUALITY;

D O I：

10.1016/j.jmaa.2011.07.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to developing augmented Lagrangian duality theory in vector optimization. By using the concepts of the supremum and infimum of a set and conjugate duality of a set-valued map on the basic of weak efficiency, we establish the interchange rules for a set-valued map, and propose an augmented Lagrangian function for a vector optimization problem with set-valued data. Under this augmented Lagrangian, weak and strong duality results are given. Then we derive sufficient conditions for penalty representations of the primal problem. The obtained results extend the corresponding theorems existing in scalar optimization. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：473 / 486

页数：14

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