Conjugate duality in set optimization via subdifferential respect to set-order relations.
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| Title: | Conjugate duality in set optimization via subdifferential respect to set-order relations. |
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| Authors: | Zhai, Yuwen1 (AUTHOR) zhaiyw7415@163.com, Yu, Guolin1 (AUTHOR) guolin_yu@126.com, Tang, Tian2 (AUTHOR) tangt6304@163.com |
| Source: | Journal of Optimization Theory & Applications. Jun2026, Vol. 209 Issue 3, p1-25. 25p. |
| Subjects: | Subdifferentials, Set-valued maps, Multi-objective optimization, Ordered sets, Duality theory (Mathematics), Mathematical optimization |
| Abstract: | Based on subdifferentials and conjugate functions, we obtain conjugate duality theorems of set optimization problem under set-order relations. This paper has two main purposes. One is to put forward a new notion of subdifferential of set-valued maps based on m-order relations, and establish some properties of the subdifferential, such as convexity, closedness and homogeneity. The other is to propose new conjugate and biconjugate maps of set-valued maps via the Minkowski difference, obtain some relations among the maps and the subdifferential, and establish optimality conditions, weak and strong conjugate duality theorems of set-order solutions to set optimization problem. Finally, we apply the main results of the paper to uncertain optimization problems. communicated by Tuyen Van Nguyen. [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.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193858474 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Conjugate duality in set optimization via subdifferential respect to set-order relations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhai%2C+Yuwen%22">Zhai, Yuwen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhaiyw7415@163.com</i><br /><searchLink fieldCode="AR" term="%22Yu%2C+Guolin%22">Yu, Guolin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> guolin_yu@126.com</i><br /><searchLink fieldCode="AR" term="%22Tang%2C+Tian%22">Tang, Tian</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> tangt6304@163.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Optimization+Theory+%26+Applications%22">Journal of Optimization Theory & Applications</searchLink>. Jun2026, Vol. 209 Issue 3, p1-25. 25p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Subdifferentials%22">Subdifferentials</searchLink><br /><searchLink fieldCode="DE" term="%22Set-valued+maps%22">Set-valued maps</searchLink><br /><searchLink fieldCode="DE" term="%22Multi-objective+optimization%22">Multi-objective optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Ordered+sets%22">Ordered sets</searchLink><br /><searchLink fieldCode="DE" term="%22Duality+theory+%28Mathematics%29%22">Duality theory (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Based on subdifferentials and conjugate functions, we obtain conjugate duality theorems of set optimization problem under set-order relations. This paper has two main purposes. One is to put forward a new notion of subdifferential of set-valued maps based on m-order relations, and establish some properties of the subdifferential, such as convexity, closedness and homogeneity. The other is to propose new conjugate and biconjugate maps of set-valued maps via the Minkowski difference, obtain some relations among the maps and the subdifferential, and establish optimality conditions, weak and strong conjugate duality theorems of set-order solutions to set optimization problem. Finally, we apply the main results of the paper to uncertain optimization problems. communicated by Tuyen Van Nguyen. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10957-026-03014-1 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 1 Subjects: – SubjectFull: Subdifferentials Type: general – SubjectFull: Set-valued maps Type: general – SubjectFull: Multi-objective optimization Type: general – SubjectFull: Ordered sets Type: general – SubjectFull: Duality theory (Mathematics) Type: general – SubjectFull: Mathematical optimization Type: general Titles: – TitleFull: Conjugate duality in set optimization via subdifferential respect to set-order relations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhai, Yuwen – PersonEntity: Name: NameFull: Yu, Guolin – PersonEntity: Name: NameFull: Tang, Tian IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00223239 Numbering: – Type: volume Value: 209 – Type: issue Value: 3 Titles: – TitleFull: Journal of Optimization Theory & Applications Type: main |
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