Optimality Conditions and Subdifferential Calculus for Infinite Sums of Functions.
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| Title: | Optimality Conditions and Subdifferential Calculus for Infinite Sums of Functions. |
|---|---|
| Authors: | Hantoute, Abderrahim1 (AUTHOR) hantoute@ua.es, Kruger, Alexander Y.2 (AUTHOR) alexanderkruger@tdtu.edu.vn, López, Marco A.1 (AUTHOR) marco.antonio@ua.es |
| Source: | Journal of Optimization Theory & Applications. Mar2026, Vol. 208 Issue 3, p1-31. 31p. |
| Subjects: | Subdifferentials, Infinite series (Mathematics), Variational principles, Mathematical functions |
| Abstract: | The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems give fuzzy subdifferential necessary conditions (multiplier rules) for a local minimum of the sum of an infinite collection of functions and fuzzy subdifferential sum rules without the traditional Lipschitz continuity assumptions. More subtle "quasi" versions of the uniform infimum and uniform lower semicontinuity properties are also discussed. [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: 191327533 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Optimality Conditions and Subdifferential Calculus for Infinite Sums of Functions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hantoute%2C+Abderrahim%22">Hantoute, Abderrahim</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hantoute@ua.es</i><br /><searchLink fieldCode="AR" term="%22Kruger%2C+Alexander+Y%2E%22">Kruger, Alexander Y.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> alexanderkruger@tdtu.edu.vn</i><br /><searchLink fieldCode="AR" term="%22López%2C+Marco+A%2E%22">López, Marco A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> marco.antonio@ua.es</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>. Mar2026, Vol. 208 Issue 3, p1-31. 31p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Subdifferentials%22">Subdifferentials</searchLink><br /><searchLink fieldCode="DE" term="%22Infinite+series+%28Mathematics%29%22">Infinite series (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+principles%22">Variational principles</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems give fuzzy subdifferential necessary conditions (multiplier rules) for a local minimum of the sum of an infinite collection of functions and fuzzy subdifferential sum rules without the traditional Lipschitz continuity assumptions. More subtle "quasi" versions of the uniform infimum and uniform lower semicontinuity properties are also discussed. [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/s10957-025-02916-w Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 31 StartPage: 1 Subjects: – SubjectFull: Subdifferentials Type: general – SubjectFull: Infinite series (Mathematics) Type: general – SubjectFull: Variational principles Type: general – SubjectFull: Mathematical functions Type: general Titles: – TitleFull: Optimality Conditions and Subdifferential Calculus for Infinite Sums of Functions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hantoute, Abderrahim – PersonEntity: Name: NameFull: Kruger, Alexander Y. – PersonEntity: Name: NameFull: López, Marco A. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00223239 Numbering: – Type: volume Value: 208 – Type: issue Value: 3 Titles: – TitleFull: Journal of Optimization Theory & Applications Type: main |
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