Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis

被引：43

作者：

Ansari, Qamrul Hasan ^{[1
,2
]}

Koebis, Elisabeth ^{[3
]}

Sharma, Pradeep Kumar ^{[1
]}

机构：

[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

[2] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran, Saudi Arabia

[3] Martin Luther Univ Halle Wittenberg, Inst Math, D-06099 Halle, Saale, Germany

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2019年 / 181卷 / 03期

关键词：

Oriented distance function; Set relations; Image space analysis; Uncertain multiobjective optimization; Robustness; 49J53; 90C29; 90C30; 90C31;

D O I：

10.1007/s10957-019-01505-y

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：

In this paper, we characterize different kinds of multiobjective robustness concepts via the well-known oriented distance function. By using characterizations of several set relations via the oriented distance function, together with the help of image space analysis, we construct some suitable subsets of the scalarization image space to obtain equivalent characterizations for various robust solutions for uncertain multiobjective optimization problems based on a set approach.

引用

页码：817 / 839

页数：23

共 34 条

[1]

[Anonymous], 2005, CONSTRAINED OPTIMIZA

[2] Characterizations of set relations with respect to variable domination structures via oriented distance function [J].

Ansari, Qamrul Hasan ;

Koebis, Elisabeth ;

Sharma, Pradeep Kumar .

OPTIMIZATION, 2018, 67 (09) :1389-1407

[3]

Ansari QH., 2018, Vector variational inequalities and vector optimization

[4]

BenTal A, 2009, PRINC SER APPL MATH, P1

[5]

BOCZKO EM, 2005, ARXIVCSLG0511105

[6] Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization [J].

Chen, Jiawei ;

Koebis, Elisabeth ;

Koebis, Markus ;

Yao, Jen-Chih .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2018, 177 (03) :816-834

[7] 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

[8] Vector Variational-Like Inequalities with Constraints: Separation and Alternative [J].

Chen, Jiawei ;

Li, Shengjie ;

Wan, Zhongping ;

Yao, Jen-Chih .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 166 (02) :460-479

[9] SHAPE-ANALYSIS VIA ORIENTED DISTANCE FUNCTIONS [J].

DELFOUR, MC ;

ZOLESIO, JP .

JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 123 (01) :129-201

[10] Oriented distance function and its evolution equation for initial sets with thin boundary [J].

Delfour, MC ;

Zolésio, JP .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2004, 42 (06) :2286-2304

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