Parametric shape optimization using the support function

Pedro R. S. Antunes () and Beniamin Bogosel ()
Additional contact information
Pedro R. S. Antunes: Universidade Aberta
Beniamin Bogosel: École Polytechnique

Computational Optimization and Applications, 2022, vol. 82, issue 1, No 5, 107-138

Abstract: Abstract The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization problems under various constraints. We propose a numerical framework in dimensions two and three and we present applications from the field of convex geometry. We consider the optimization of functionals depending on the volume, perimeter and Dirichlet Laplace eigenvalues under the aforementioned constraints. In particular we confirm numerically Meissner’s conjecture, regarding three dimensional bodies of constant width with minimal volume.

Keywords: Shape optimization; Support function; Numerical simulations; Convexity (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00360-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00360-4

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-022-00360-4

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().