Scalarization and convergence in unified set optimization

被引：4

作者：

Khushboo ^{[1
]}

Lalitha, C. S. ^{[2
]}

机构：

[1] Univ Delhi, Dept Math, Delhi 110007, India

[2] Univ Delhi, Dept Math, South Campus,Benito Juarez Rd, New Delhi 110021, India

来源：

RAIRO-OPERATIONS RESEARCH | 2021年 / 55卷 / 06期

关键词：

Unified set optimization; nonlinear scalarization; oriented distance function; semicontinuity; Painleve-Kuratowski convergence; VECTOR OPTIMIZATION; WELL-POSEDNESS; STABILITY; EFFICIENCY; DISTANCE; THEOREMS;

D O I：

10.1051/ro/2021169

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：

This paper deals with scalarization and stability aspects for a unified set optimization problem. We provide characterization for a unified preference relation and the corresponding unified minimal solution in terms of a generalized oriented distance function of the sup-inf type. We establish continuity of a function associated with the generalized oriented distance function and provide an existence result for the unified minimal solution. We establish Painleve-Kuratowski convergence of minimal solutions of a family of scalar problems to the minimal solutions of the unified set optimization problem.

引用

收藏

页码：3603 / 3616

页数：14

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