Optimal design of sensors via geometric criteria

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dc.contributor.authorFtouhi, Ilias
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2025-06-12T11:43:02Z
dc.date.available2025-06-12T11:43:02Z
dc.date.issued2023-05-23
dc.date.updated2025-06-12T11:43:02Z
dc.description.abstractWe consider a convex set Ω and look for the optimal convex sensor ω⊂ Ω of a given measure that minimizes the maximal distance to the points of Ω. This problem can be written as follows inf{dH(ω,Ω)||ω|=candω⊂Ω}, where c∈ (0 , | Ω |) , dH being the Hausdorff distance. We show that the parametrization via the support functions allows us to formulate the geometric optimal shape design problem as an analytic one. By proving a judicious equivalence result, the shape optimization problem is approximated by a simpler minimization problem of a quadratic function under linear constraints. We then present some numerical results and qualitative properties of the optimal sensors and exhibit an unexpected symmetry breaking phenomenon.en
dc.description.sponsorshipI. Ftouhi is supported by the Alexander von Humboldt Foundation and has been partially supported by the project ANR-18-CE40-0013 SHAPO financed by the French Agence Nationale de la Recherche (ANR). E. Zuazua has been funded by the Alexander von Humboldt-Professorship program, the ModConFlex Marie Curie Action, HORIZON-MSCA-2021-DN-01, the COST Action MAT-DYN-NET, the Transregio 154 Project “Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks” of the DFG, grants PID2020-112617GB-C22 and TED2021-131390B-I00 of MINECO (Spain), and by the Madrid Government-UAM Agreement for the Excellence of the University Research Stay in the context of the VPRICIT (Regional Programme of Research and Technological Innovation)en
dc.identifier.citationFtouhi, I., & Zuazua, E. (2023). Optimal design of sensors via geometric criteria. Journal of Geometric Analysis, 33(8). https://doi.org/10.1007/S12220-023-01301-1
dc.identifier.doi10.1007/S12220-023-01301-1
dc.identifier.issn1050-6926
dc.identifier.urihttp://hdl.handle.net/20.500.14454/3033
dc.language.isoeng
dc.publisherSpringer
dc.rights© The Author(s) 2023
dc.subject.otherConvex geometry
dc.subject.otherSensor design
dc.subject.otherShape optimization
dc.titleOptimal design of sensors via geometric criteriaen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.issue8
oaire.citation.titleJournal of Geometric Analysis
oaire.citation.volume33
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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