A Hausdorff-type distance, the Clarke generalized directional derivative and applications in set optimization problems

被引：12

作者：

Han, Yu ^{[1
]}

机构：

[1] Jiangxi Univ Finance & Econ, Sch Stat, Nanchang, Jiangxi, Peoples R China

来源：

APPLICABLE ANALYSIS | 2022年 / 101卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Set optimization problem; nonlinear scalarizing function; Hausdorff-type distance; Clarke generalized directional derivative; ORDER RELATIONS; SCALARIZATION;

D O I：

10.1080/00036811.2020.1778673

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a Hausdorff-type distance relative to an ordering cone between two sets. We obtain some properties of the Hausdorff-type distance. In particular, we give a characterization of the Hausdorff-type distance. Moreover, we introduce the Clarke generalized directional derivative for set-valued mappings by using the nonlinear scalarizing function forl-type less order relation, which is introduced by Hernandez and Rodriguez-Marin [Nonconvex scalarization in set optimization with set-valued maps. J Math Anal Appl. 2007;325:1-18]. Some properties of the Clarke generalized directional derivative are given. As applications, we present necessary and sufficient optimality conditions for set optimization problems.

引用

页码：1243 / 1260

页数：18

共 22 条

[1] Characterizations of set relations with respect to variable domination structures via oriented distance function
Ansari, Qamrul Hasan
Koebis, Elisabeth
Sharma, Pradeep Kumar
[J]. OPTIMIZATION, 2018, 67 (09) : 1389 - 1407
[2] Characterizations of set order relations and constrained set optimization problems via oriented distance function
Chen, Jiawei
Ansari, Qamrul Hasan
Yao, Jen-Chih
[J]. OPTIMIZATION, 2017, 66 (11) : 1741 - 1754
[3] GENERALIZED GRADIENTS AND APPLICATIONS
CLARKE, FH
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 205 (APR) : 247 - 262
[4] Clarke FH., 1983, SIAM CLASSICS APPL M, V5
[5] Set Approach for Set Optimization with Variable Ordering Structures Part II: Scalarization Approaches
Eichfelder, Gabriele
Pilecka, Maria
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 171 (03) : 947 - 963
[6] Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach
Eichfelder, Gabriele
Pilecka, Maria
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 171 (03) : 931 - 946
[7] NONCONVEX SEPARATION THEOREMS AND SOME APPLICATIONS IN VECTOR OPTIMIZATION
GERTH, C
WEIDNER, P
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1990, 67 (02) : 297 - 320
[8] Gopfert A., 2003, VARIATIONAL METHODS
[9] Nonlinear scalarizing functions in set optimization problems
Han, Yu
[J]. OPTIMIZATION, 2019, 68 (09) : 1685 - 1718
[10] Continuity and Convexity of a Nonlinear Scalarizing Function in Set Optimization Problems with Applications
Han, Yu
Huang, Nan-jing
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2018, 177 (03) : 679 - 695

← 1 2 3 →