Well-Posedness of Set Optimization Problems with Set Order Defined by Minkowski Difference

Zhiang Zhou; Kehao Feng; Qamrul Hasan Ansari

doi:10.1007/s10957-025-02608-5

Well-Posedness of Set Optimization Problems with Set Order Defined by Minkowski Difference

Zhiang Zhou^*
, Kehao Feng
, Qamrul Hasan Ansari

^*Corresponding author for this work

Department of Mathematics

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

8 Scopus citations

Abstract

In this paper, we consider set optimization problems whose solution concepts are defined by means of set less order relations involving Minkwoski difference. We propose well-posedness and generalized well-posedness for set optimization problems, and derive sufficient and necessary conditions for these well-posedness. A relation between well-posedness and generalized well-posedness for set optimization problems is also given. We use a nonlinear scalarization method to establish necessary and sufficient conditions for the well-posedness and generalized well-posedness of set optimization problems. Several examples are given to illustrate our results.

Original language	English
Article number	31
Journal	Journal of Optimization Theory and Applications
Volume	204
Issue number	2
DOIs	https://doi.org/10.1007/s10957-025-02608-5
State	Published - Feb 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

Keywords

Scalarization
Set optimization problems
Set order relations
Well-posedness

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

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10.1007/s10957-025-02608-5

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title = "Well-Posedness of Set Optimization Problems with Set Order Defined by Minkowski Difference",

abstract = "In this paper, we consider set optimization problems whose solution concepts are defined by means of set less order relations involving Minkwoski difference. We propose well-posedness and generalized well-posedness for set optimization problems, and derive sufficient and necessary conditions for these well-posedness. A relation between well-posedness and generalized well-posedness for set optimization problems is also given. We use a nonlinear scalarization method to establish necessary and sufficient conditions for the well-posedness and generalized well-posedness of set optimization problems. Several examples are given to illustrate our results.",

keywords = "Scalarization, Set optimization problems, Set order relations, Well-posedness",

author = "Zhiang Zhou and Kehao Feng and Ansari, \{Qamrul Hasan\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.",

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doi = "10.1007/s10957-025-02608-5",

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AU - Zhou, Zhiang

AU - Feng, Kehao

AU - Ansari, Qamrul Hasan

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/2

Y1 - 2025/2

N2 - In this paper, we consider set optimization problems whose solution concepts are defined by means of set less order relations involving Minkwoski difference. We propose well-posedness and generalized well-posedness for set optimization problems, and derive sufficient and necessary conditions for these well-posedness. A relation between well-posedness and generalized well-posedness for set optimization problems is also given. We use a nonlinear scalarization method to establish necessary and sufficient conditions for the well-posedness and generalized well-posedness of set optimization problems. Several examples are given to illustrate our results.

AB - In this paper, we consider set optimization problems whose solution concepts are defined by means of set less order relations involving Minkwoski difference. We propose well-posedness and generalized well-posedness for set optimization problems, and derive sufficient and necessary conditions for these well-posedness. A relation between well-posedness and generalized well-posedness for set optimization problems is also given. We use a nonlinear scalarization method to establish necessary and sufficient conditions for the well-posedness and generalized well-posedness of set optimization problems. Several examples are given to illustrate our results.

KW - Scalarization

KW - Set optimization problems

KW - Set order relations

KW - Well-posedness

UR - https://www.scopus.com/pages/publications/85218124637

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DO - 10.1007/s10957-025-02608-5

M3 - Article

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SN - 0022-3239

VL - 204

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 2

M1 - 31

ER -

Well-Posedness of Set Optimization Problems with Set Order Defined by Minkowski Difference

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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