Well-Posedness of Set Optimization Problems with Set Order Defined by Minkowski Difference

被引：0
作者：
Zhou, Zhiang [1 ]
Feng, Kehao [1 ]
Ansari, Qamrul Hasan [1 ,2 ]
机构：
[1] Chongqing Univ Technol, Coll Sci, Chongqing 400054, Peoples R China
[2] King Fahd Univ Petr & Minerals, Dept Math, Dhahran 31261, Saudi Arabia
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2025年 / 204卷 / 02期
关键词：
Set optimization problems; Set order relations; Well-posedness; Scalarization; SCALARIZATION; CONVEXITY; POINTWISE;
D O I：
10.1007/s10957-025-02608-5
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 consider set optimization problems whose solution concepts are defined by means of set less order relations involving Minkwoski difference. We propose well-posedness and generalized well-posedness for set optimization problems, and derive sufficient and necessary conditions for these well-posedness. A relation between well-posedness and generalized well-posedness for set optimization problems is also given. We use a nonlinear scalarization method to establish necessary and sufficient conditions for the well-posedness and generalized well-posedness of set optimization problems. Several examples are given to illustrate our results.
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页数：24
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