Optimality conditions for global minimizers to a class of convex set optimization problem subjected to geometric constraints.
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| Title: | Optimality conditions for global minimizers to a class of convex set optimization problem subjected to geometric constraints. |
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| Authors: | Nguyen, Minh Tung1 (AUTHOR) tungnm@hub.edu.vn, Pham, Thanh Duoc2 (AUTHOR), Nguyen, Van Hoi3,4 (AUTHOR) |
| Source: | RAIRO: Operations Research (2804-7303). 2025, Vol. 59 Issue 2, p1019-1034. 16p. |
| Subjects: | Convex sets, Directional derivatives, Nonlinear functions, Calculus |
| Abstract: | In this paper, we study optimality conditions for both global and approximate minimizers to convex set optimization problems with geometric constraints. We first consider a form of Gerstewitz's nonlinear scalarization function concerning the set-less relation introduced by Kuroiwa. Then, it is employed to construct a type of directional derivative and sub-gradient for cone-convex set-valued maps. We also give some properties and usual calculus rules for these concepts. Later, some necessary and sufficient conditions for global and approximate solutions are established. Examples are provided for analyzing and illustrating the obtained results. [ABSTRACT FROM AUTHOR] |
| Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences 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 | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 185034300 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Optimality conditions for global minimizers to a class of convex set optimization problem subjected to geometric constraints. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Nguyen%2C+Minh+Tung%22">Nguyen, Minh Tung</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> tungnm@hub.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Pham%2C+Thanh+Duoc%22">Pham, Thanh Duoc</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Nguyen%2C+Van+Hoi%22">Nguyen, Van Hoi</searchLink><relatesTo>3,4</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22RAIRO%3A+Operations+Research+%282804-7303%29%22">RAIRO: Operations Research (2804-7303)</searchLink>. 2025, Vol. 59 Issue 2, p1019-1034. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Convex+sets%22">Convex sets</searchLink><br /><searchLink fieldCode="DE" term="%22Directional+derivatives%22">Directional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+functions%22">Nonlinear functions</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus%22">Calculus</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we study optimality conditions for both global and approximate minimizers to convex set optimization problems with geometric constraints. We first consider a form of Gerstewitz's nonlinear scalarization function concerning the set-less relation introduced by Kuroiwa. Then, it is employed to construct a type of directional derivative and sub-gradient for cone-convex set-valued maps. We also give some properties and usual calculus rules for these concepts. Later, some necessary and sufficient conditions for global and approximate solutions are established. Examples are provided for analyzing and illustrating the obtained results. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=185034300 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1051/ro/2025025 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 1019 Subjects: – SubjectFull: Convex sets Type: general – SubjectFull: Directional derivatives Type: general – SubjectFull: Nonlinear functions Type: general – SubjectFull: Calculus Type: general Titles: – TitleFull: Optimality conditions for global minimizers to a class of convex set optimization problem subjected to geometric constraints. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Nguyen, Minh Tung – PersonEntity: Name: NameFull: Pham, Thanh Duoc – PersonEntity: Name: NameFull: Nguyen, Van Hoi IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 28047303 Numbering: – Type: volume Value: 59 – Type: issue Value: 2 Titles: – TitleFull: RAIRO: Operations Research (2804-7303) Type: main |
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