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Strict Efficiency in Set Optimization Studied with the Set Approach.

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Title: Strict Efficiency in Set Optimization Studied with the Set Approach.
Authors: Ha, Truong Xuan Duc1 (AUTHOR) hatxd@thanglong.edu.vn
Source: Journal of Optimization Theory & Applications. May2025, Vol. 205 Issue 2, p1-20. 20p.
Subjects: Directional derivatives, Subdifferentials, Set-valued maps
Abstract: This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the l-type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solutions are obtained. In particular, we establish some conditions expressed in terms of a high-order directional derivative of set-valued maps and the (convex or limiting) subdifferentials, normal cones and coderivatives. Various illustrating examples are presented. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Strict Efficiency in Set Optimization Studied with the Set Approach.
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  Data: <searchLink fieldCode="AR" term="%22Ha%2C+Truong+Xuan+Duc%22">Ha, Truong Xuan Duc</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hatxd@thanglong.edu.vn</i>
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  Data: <searchLink fieldCode="DE" term="%22Directional+derivatives%22">Directional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Subdifferentials%22">Subdifferentials</searchLink><br /><searchLink fieldCode="DE" term="%22Set-valued+maps%22">Set-valued maps</searchLink>
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  Data: This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the l-type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solutions are obtained. In particular, we establish some conditions expressed in terms of a high-order directional derivative of set-valued maps and the (convex or limiting) subdifferentials, normal cones and coderivatives. Various illustrating examples are presented. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10957-025-02617-4
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        Text: English
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        PageCount: 20
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      – SubjectFull: Directional derivatives
        Type: general
      – SubjectFull: Subdifferentials
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      – SubjectFull: Set-valued maps
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              M: 05
              Text: May2025
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