Existence and connectedness of the l-minimal approximate solutions for set optimization problems: an application in generalized multiobjective robustness

被引：0
作者：
Madhusudan Das
C. Nahak
M. P. Biswal
机构：
[1] Indian Institute of Technology Kharagpur,Department of Mathematics
来源：
The Journal of Analysis | 2024年 / 32卷
关键词：
Set optimization problem; Scalarization; Approximate solution; Connectedness; Robustness; 49J53; 90C29; 90C31;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The goal of this paper is to study the existence and connectedness of the l-minimal approximate solutions of the set-valued optimization problem using an extended signed distance function. The existence of the l-minimal approximate solutions is established by virtue of the FAN-KKM and Cantor’s intersection theorems. A scalarization result of the set of l-minimal approximate solutions is proposed without adopting the convexity notion of the objective function. By using this scalarization result, we explore the (path) connectedness of the l-minimal approximate solutions. Moreover, we apply our approach to generalized multiobjective robustness problems. Some necessary examples are illustrated to validate our main results.
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页码：373 / 398
页数：25
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