Stability of efficient solutions to set optimization problems

被引：0
作者：
L. Q. Anh
T. Q. Duy
D. V. Hien
机构：
[1] Cantho University,Department of Mathematics, Teacher College
[2] Ton Duc Thang University,Division of Computational Mathematics and Engineering, Institute for Computational Science
[3] Ton Duc Thang University,Faculty of Mathematics and Statistics
[4] University of Science,Faculty of Mathematics and Computer Science
[5] Vietnam National University,Department of Mathematics
[6] Ho Chi Minh City University of Food Industry,undefined
来源：
Journal of Global Optimization | 2020年 / 78卷
关键词：
Set optimization problem; Pareto minimal solution; Internal and external stability; Compact convergence; Domination property; 49K40; 65K10; 90C29; 90C30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This article deals with considering stability properties of Pareto minimal solutions to set optimization problems with the set less order relation in real topological Hausdorff vector spaces. We focus on studying the Painlevé–Kuratowski convergence of Pareto minimal elements in the image space. Employing convexity properties, we study the external stability of Pareto minimal solutions via weak ones. Then, we use converse properties to investigate external stability conditions to such problems where Pareto minimal solution sets and weak/ideal ones are distinct. For the internal stability, we propose a concept of compact convergence in the sense of Painlevé–Kuratowski and use it together with a domination property to analyze stability conditions for the reference problems.
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页码：563 / 580
页数：17
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