Directional derivative for set-valued maps with weighted set order relations

Qamrul Hasan Ansari; Mohd Lukman; Pradeep Kumar Sharma

doi:10.1080/02331934.2024.2436561

Directional derivative for set-valued maps with weighted set order relations

Qamrul Hasan Ansari^*
, Mohd Lukman
, Pradeep Kumar Sharma

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we first introduce a Hausdorff-type distance by means of a nonlinear scalarization function related to the weighted set order relations, and examine some of its properties. We then use it to define directional derivative for set-valued maps, and derive some of its properties similar to the scalar case. As applications, we obtain necessary and sufficient optimality conditions for set optimization problems. Several examples are given to illustrate our results and the concepts introduced in this paper.

Original language	English
Journal	Optimization
DOIs	https://doi.org/10.1080/02331934.2024.2436561
State	Accepted/In press - 2024
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2024 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Hausdorff-type distance
Weighted set relations
directional derivative
optimality conditions
set optimization

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

Access to Document

10.1080/02331934.2024.2436561

Cite this

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title = "Directional derivative for set-valued maps with weighted set order relations",

abstract = "In this paper, we first introduce a Hausdorff-type distance by means of a nonlinear scalarization function related to the weighted set order relations, and examine some of its properties. We then use it to define directional derivative for set-valued maps, and derive some of its properties similar to the scalar case. As applications, we obtain necessary and sufficient optimality conditions for set optimization problems. Several examples are given to illustrate our results and the concepts introduced in this paper.",

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AU - Sharma, Pradeep Kumar

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N2 - In this paper, we first introduce a Hausdorff-type distance by means of a nonlinear scalarization function related to the weighted set order relations, and examine some of its properties. We then use it to define directional derivative for set-valued maps, and derive some of its properties similar to the scalar case. As applications, we obtain necessary and sufficient optimality conditions for set optimization problems. Several examples are given to illustrate our results and the concepts introduced in this paper.

AB - In this paper, we first introduce a Hausdorff-type distance by means of a nonlinear scalarization function related to the weighted set order relations, and examine some of its properties. We then use it to define directional derivative for set-valued maps, and derive some of its properties similar to the scalar case. As applications, we obtain necessary and sufficient optimality conditions for set optimization problems. Several examples are given to illustrate our results and the concepts introduced in this paper.

KW - Hausdorff-type distance

KW - Weighted set relations

KW - directional derivative

KW - optimality conditions

KW - set optimization

UR - https://www.scopus.com/pages/publications/85210954572

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M3 - Article

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SN - 0233-1934

JO - Optimization

JF - Optimization

ER -

Directional derivative for set-valued maps with weighted set order relations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this