Partial order relations on family of sets and scalarizations for set optimization

被引：1
作者：
Emrah Karaman
Mustafa Soyertem
İlknur Atasever Güvenç
Didem Tozkan
Mahide Küçük
Yalçın Küçük
机构：
[1] Anadolu University,Department of Mathematics, Faculty of Science
[2] Uşak University,Department of Mathematics, Faculty of Art and Science
来源：
Positivity | 2018年 / 22卷
关键词：
Set optimization; Partial order; Scalarization; Optimality conditions; 80M50; 90C26;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this study, some new order relations on family of sets are introduced by using Minkowski difference. The relations between these orders and the ordering cone of the vector space are obtained. It is shown that depending on the corresponding cone, these order relations are partial orders on the family of nonempty bounded sets. Some relationships between these order relations and upper and lower set less order relations are investigated. Also, two scalarizing functions are introduced in order to replace set optimization problems with respect to these partial order relations with scalar optimization problems. Moreover, necessary and sufficient optimality conditions are presented.
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页码：783 / 802
页数：19
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