Essential stability in set optimization

被引：6
作者：
Karuna [1 ]
Lalitha, C. S. [2 ]
机构：
[1] Univ Delhi, Dept Math, Delhi, India
[2] Univ Delhi, Dept Math, South Campus, New Delhi, India
来源：
OPTIMIZATION | 2022年 / 71卷 / 07期
关键词：
Set optimization; essential set; minimal essential set; strict quasiconvexity; essentially minimal set; ESSENTIAL COMPONENTS; WELL-POSEDNESS;
D O I：
10.1080/02331934.2020.1836635
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：
The objective of the paper is to study essential stability in set optimization. Essential sets of efficient and weak efficient solution sets are introduced for a set optimization problem and essential sets are identified for both the solution sets. A characterization of essential sets is given for efficient solution sets. Finally, sufficient conditions are provided for the existence of essential sets in the image space.
引用
收藏
页码：1803 / 1816
页数：14
相关论文
共 29 条
[1]   ESSENTIAL AND NON ESSENTIAL FIXED POINTS [J].
FORT, MK .
AMERICAN JOURNAL OF MATHEMATICS, 1950, 72 (02) :315-322
[2]   Stability of minimizers of set optimization problems [J].
Gaydu, Michael ;
Geoffroy, Michel H. ;
Jean-Alexis, Celia ;
Nedelcheva, Diana .
POSITIVITY, 2017, 21 (01) :127-141
[3]   Convergence of Solutions of a Set Optimization Problem in the Image Space [J].
Gutierrez, Cesar ;
Miglierina, Enrico ;
Molho, Elena ;
Novo, Vicente .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 170 (02) :358-371
[4]   Well-posedness and stability of solutions for set optimization problems [J].
Han, Yu ;
Huang, Nan-jing .
OPTIMIZATION, 2017, 66 (01) :17-33
[5]   Nonconvex scalarization in set optimization with set-valued maps [J].
Hernandez, E. ;
Rodriguez-Marin, L. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (01) :1-18
[6]   Existence theorems for set optimization problems [J].
Hernandez, Elvira ;
Rodriguez-Marin, Luis .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (06) :1726-1736
[7]  
Jahn J., 2004, Vector optimization : theory, applications, and extensions
[8]   New Order Relations in Set Optimization [J].
Jahn, Johannes ;
Truong Xuan Duc Ha .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 148 (02) :209-236
[9]   External and internal stability in set optimization [J].
Karuna ;
Lalitha, C. S. .
OPTIMIZATION, 2019, 68 (04) :833-852
[10]  
Karuna, 2018, J NONLINEAR CONVEX A, V19, P1247
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