Subdifferentials at infinity and applications in optimization.
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| Title: | Subdifferentials at infinity and applications in optimization. |
|---|---|
| Authors: | Kim, Do Sang1 (AUTHOR) dskim@pknu.ac.kr, Nguyen, Minh Tùng2 (AUTHOR) tungnm@hub.edu.vn, Pham, Tien-Son3 (AUTHOR) sonpt@dlu.edu.vn |
| Source: | Mathematical Programming. Nov2025, Vol. 214 Issue 1/2, p409-440. 32p. |
| Subjects: | Mathematical optimization, Infinity (Mathematics), Cones, Subdifferentials, Lipschitz continuity |
| Abstract: | In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions are established. A complete characterization of the Lipschitz continuity at infinity for lower semicontinuous functions is given. The obtained results are aimed ultimately at applications to diverse problems of optimization, such as optimality conditions, coercive properties, weak sharp minima and stability results. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Programming 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 189704701 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Subdifferentials at infinity and applications in optimization. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kim%2C+Do+Sang%22">Kim, Do Sang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> dskim@pknu.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Nguyen%2C+Minh+Tùng%22">Nguyen, Minh Tùng</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> tungnm@hub.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Pham%2C+Tien-Son%22">Pham, Tien-Son</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> sonpt@dlu.edu.vn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Programming%22">Mathematical Programming</searchLink>. Nov2025, Vol. 214 Issue 1/2, p409-440. 32p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Infinity+%28Mathematics%29%22">Infinity (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Cones%22">Cones</searchLink><br /><searchLink fieldCode="DE" term="%22Subdifferentials%22">Subdifferentials</searchLink><br /><searchLink fieldCode="DE" term="%22Lipschitz+continuity%22">Lipschitz continuity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions are established. A complete characterization of the Lipschitz continuity at infinity for lower semicontinuous functions is given. The obtained results are aimed ultimately at applications to diverse problems of optimization, such as optimality conditions, coercive properties, weak sharp minima and stability results. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Programming 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/s10107-024-02187-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 32 StartPage: 409 Subjects: – SubjectFull: Mathematical optimization Type: general – SubjectFull: Infinity (Mathematics) Type: general – SubjectFull: Cones Type: general – SubjectFull: Subdifferentials Type: general – SubjectFull: Lipschitz continuity Type: general Titles: – TitleFull: Subdifferentials at infinity and applications in optimization. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kim, Do Sang – PersonEntity: Name: NameFull: Nguyen, Minh Tùng – PersonEntity: Name: NameFull: Pham, Tien-Son IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00255610 Numbering: – Type: volume Value: 214 – Type: issue Value: 1/2 Titles: – TitleFull: Mathematical Programming Type: main |
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