Levitin-Polyak Well-Posedness for Parametric Set Optimization Problem

被引：1

作者：

Tahu, Biswajit ^{[1
]}

Dhingra, Mansi ^{[1
]}

Kumar, Satish ^{[1
]}

Garg, Pankaj Kumar ^{[2
]}

机构：

[1] Univ Delhi, Dept Math, Delhi 110007, India

[2] Univ Delhi, Dept Math, Rajdhani Coll, New Delhi 110015, India

来源：

CARPATHIAN JOURNAL OF MATHEMATICS | 2023年 / 39卷 / 02期

关键词：

Parametric set optimization problem; l-weak minimal solution; Levitin-Polyak well-posedness; Upper Hausdorff convergence; Painleve-Kuratowski convergence; SCALARIZATION; CONVEXITY; POINTWISE; STABILITY;

D O I：

10.37193/CJM.2023.02.12

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to introduce two notions of Levitin-Polyak (LP in short) well-posedness for a parametric set optimization problem, a pointwise and a global notion. Necessary and sufficient conditions for a parametric set optimization problem to be LP well-posed are given. Characterizations of LP well-posedness for a parametric set optimization problem in terms of upper Hausdorff convergence and Painleve-Kuratowski convergence of sequences of approximate solution sets are also established.

引用

页码：511 / 527

页数：17

共 34 条

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