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

页码：3603 / 3616

页数：14

共 37 条

[1]

[Anonymous], 2010, P 6 INT C NONL AN CO

[2] Solution semicontinuity of parametric generalized vector equilibrium problems [J].

Chen, C. R. ;

Li, S. J. ;

Teo, K. L. .

JOURNAL OF GLOBAL OPTIMIZATION, 2009, 45 (02) :309-318

[3] Vector equilibrium problems under improvement sets and linear scalarization with stability applications [J].

Chen, Chun-Rong ;

Zuo, Xin ;

Lu, Fang ;

Li, Sheng-Jie .

OPTIMIZATION METHODS & SOFTWARE, 2016, 31 (06) :1240-1257

[4] Characterizations of set order relations and constrained set optimization problems via oriented distance function [J].

Chen, Jiawei ;

Ansari, Qamrul Hasan ;

Yao, Jen-Chih .

OPTIMIZATION, 2017, 66 (11) :1741-1754

[5] Approximate solutions and scalarization in set-valued optimization [J].

Dhingra, Mansi ;

Lalitha, C. S. .

OPTIMIZATION, 2017, 66 (11) :1793-1805

[6] Characterizing Efficiency on Infinite-dimensional Commodity Spaces with Ordering Cones Having Possibly Empty Interior [J].

Flores-Bazan, Fabian ;

Flores-Bazan, Fernando ;

Laengle, Sigifredo .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 164 (02) :455-478

[7] A unified vector optimization problem: complete scalarizations and applications [J].

Flores-Bazan, Fabian ;

Hernandez, Elvira .

OPTIMIZATION, 2011, 60 (12) :1399-1419

[8] NONCONVEX SEPARATION THEOREMS AND SOME APPLICATIONS IN VECTOR OPTIMIZATION [J].

GERTH, C ;

WEIDNER, P .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1990, 67 (02) :297-320

[9] 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

[10] Continuity and Convexity of a Nonlinear Scalarizing Function in Set Optimization Problems with Applications [J].

Han, Yu ;

Huang, Nan-jing .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2018, 177 (03) :679-695

← 1 2 3 4 →