Directional Derivative of the Value Function for Parametric Set-Constrained Optimization Problems.
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| Title: | Directional Derivative of the Value Function for Parametric Set-Constrained Optimization Problems. |
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| Authors: | Bai, Kuang1 (AUTHOR), Ye, Jane J.2 (AUTHOR) janeye@uvic.ca |
| Source: | Journal of Optimization Theory & Applications. Nov2024, Vol. 203 Issue 2, p1355-1384. 30p. |
| Subjects: | Derivatives (Mathematics), Directional derivatives, Sensitivity analysis |
| Abstract: | This paper is concerned with the directional derivative of the value function for a very general set-constrained optimization problem under perturbation. Under reasonable assumptions, we obtain upper and lower estimates for the upper and lower Dini directional derivative of the value function respectively, from which we obtain Hadamard directional differentiability of the value function when the set of multipliers is a singleton. Our results do not require convexity of the set involved. Even in the case of a parametric nonlinear program, our results improve the classical ones in that our regularity conditions are weaker and the directional solution set is used which is in general smaller than its nondirectional counterparts. [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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 180830510 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Directional Derivative of the Value Function for Parametric Set-Constrained Optimization Problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bai%2C+Kuang%22">Bai, Kuang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ye%2C+Jane+J%2E%22">Ye, Jane J.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> janeye@uvic.ca</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>. Nov2024, Vol. 203 Issue 2, p1355-1384. 30p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Derivatives+%28Mathematics%29%22">Derivatives (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Directional+derivatives%22">Directional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Sensitivity+analysis%22">Sensitivity analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper is concerned with the directional derivative of the value function for a very general set-constrained optimization problem under perturbation. Under reasonable assumptions, we obtain upper and lower estimates for the upper and lower Dini directional derivative of the value function respectively, from which we obtain Hadamard directional differentiability of the value function when the set of multipliers is a singleton. Our results do not require convexity of the set involved. Even in the case of a parametric nonlinear program, our results improve the classical ones in that our regularity conditions are weaker and the directional solution set is used which is in general smaller than its nondirectional counterparts. [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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=180830510 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10957-024-02469-4 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 30 StartPage: 1355 Subjects: – SubjectFull: Derivatives (Mathematics) Type: general – SubjectFull: Directional derivatives Type: general – SubjectFull: Sensitivity analysis Type: general Titles: – TitleFull: Directional Derivative of the Value Function for Parametric Set-Constrained Optimization Problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bai, Kuang – PersonEntity: Name: NameFull: Ye, Jane J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 00223239 Numbering: – Type: volume Value: 203 – Type: issue Value: 2 Titles: – TitleFull: Journal of Optimization Theory & Applications Type: main |
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