PDE-constrained shape optimization with first-order and Newton-type methods in the W1,∞ topology.
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| Title: | PDE-constrained shape optimization with first-order and Newton-type methods in the W1,∞ topology. |
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| Authors: | Deckelnick, Klaus1 (AUTHOR), Herbert, Philip J.2 (AUTHOR) p.herbert@sussex.ac.uk, Hinze, Michael3 (AUTHOR) |
| Source: | Optimization Methods & Software. Aug2026, Vol. 41 Issue 4, p868-894. 27p. |
| Subjects: | Method of steepest descent (Numerical analysis), Newton-Raphson method, Functional analysis, Function spaces, Structural optimization, Numerical analysis |
| Abstract: | We present a general shape optimization framework based on the method of mappings in the $ W^{1,\infty } $ W 1 , ∞ topology. We propose steepest descent and Newton-like minimization algorithms for the numerical solution of the respective shape optimization problems. Our work is built upon previous work of the authors in Deckelnick, Herbert, and Hinze, ESAIM: COCV 28 (2022), where a $ W^{1,\infty } $ W 1 , ∞ framework for star-shaped domains is proposed. To illustrate our approach, we present a selection of PDE-constrained shape optimization problems and compare our findings to results from so far classical Hilbert space methods and recent p-approximations. [ABSTRACT FROM AUTHOR] |
| Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd 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: 197072089 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: PDE-constrained shape optimization with first-order and Newton-type methods in the W<superscript>1,∞</superscript> topology. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Deckelnick%2C+Klaus%22">Deckelnick, Klaus</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Herbert%2C+Philip+J%2E%22">Herbert, Philip J.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> p.herbert@sussex.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Hinze%2C+Michael%22">Hinze, Michael</searchLink><relatesTo>3</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Optimization+Methods+%26+Software%22">Optimization Methods & Software</searchLink>. Aug2026, Vol. 41 Issue 4, p868-894. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Method+of+steepest+descent+%28Numerical+analysis%29%22">Method of steepest descent (Numerical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+analysis%22">Functional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Function+spaces%22">Function spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We present a general shape optimization framework based on the method of mappings in the $ W^{1,\infty } $ W 1 , ∞ topology. We propose steepest descent and Newton-like minimization algorithms for the numerical solution of the respective shape optimization problems. Our work is built upon previous work of the authors in Deckelnick, Herbert, and Hinze, ESAIM: COCV 28 (2022), where a $ W^{1,\infty } $ W 1 , ∞ framework for star-shaped domains is proposed. To illustrate our approach, we present a selection of PDE-constrained shape optimization problems and compare our findings to results from so far classical Hilbert space methods and recent p-approximations. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd 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: 10.1080/10556788.2024.2424525 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 868 Subjects: – SubjectFull: Method of steepest descent (Numerical analysis) Type: general – SubjectFull: Newton-Raphson method Type: general – SubjectFull: Functional analysis Type: general – SubjectFull: Function spaces Type: general – SubjectFull: Structural optimization Type: general – SubjectFull: Numerical analysis Type: general Titles: – TitleFull: PDE-constrained shape optimization with first-order and Newton-type methods in the W1,∞ topology. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Deckelnick, Klaus – PersonEntity: Name: NameFull: Herbert, Philip J. – PersonEntity: Name: NameFull: Hinze, Michael IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10556788 Numbering: – Type: volume Value: 41 – Type: issue Value: 4 Titles: – TitleFull: Optimization Methods & Software Type: main |
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