Scalarization method for Levitin-Polyak well-posedness of vectorial optimization problems

被引：11

作者：

Zhu, Li ^{[1
]}

Xia, Fu-quan ^{[1
]}

机构：

[1] Sichuan Normal Univ, Dept Math, Chengdu 610066, Sichuan, Peoples R China

来源：

MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2012年 / 76卷 / 03期

基金：

国家教育部博士点专项基金资助; 中国国家自然科学基金;

关键词：

Levitin-Polyak well-posedness; Non-linear scalarization function; Optimization problems;

D O I：

10.1007/s00186-012-0410-9

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 develop a method of study of Levitin-Polyak well-posedness notions for vector valued optimization problems using a class of scalar optimization problems. We first introduce a non-linear scalarization function and consider its corresponding properties. We also introduce the Furi-Vignoli type measure and Dontchev-Zolezzi type measure to scalar optimization problems and vectorial optimization problems, respectively. Finally, we construct the equivalence relations between the Levitin-Polyak well-posedness of scalar optimization problems and the vectorial optimization problems.

引用

页码：361 / 375

页数：15

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