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

被引：0

作者：

Das, Madhusudan ^{[1
]}

Nahak, C. ^{[1
]}

Biswal, M. P. ^{[1
]}

机构：

[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India

来源：

JOURNAL OF ANALYSIS | 2024年 / 32卷 / 01期

关键词：

Set optimization problem; Scalarization; Approximate solution; Connectedness; Robustness; VALUED MAPS; CONVEXITY; DISTANCE; HENIG;

D O I：

10.1007/s41478-023-00655-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：373 / 398

页数：26