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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 10556788 |
| DOI: | 10.1080/10556788.2024.2424525 |
