Ftouhi, IliasZuazua, Enrique2025-06-122025-06-122023-05-23Ftouhi, I., & Zuazua, E. (2023). Optimal design of sensors via geometric criteria. Journal of Geometric Analysis, 33(8). https://doi.org/10.1007/S12220-023-01301-11050-692610.1007/S12220-023-01301-1http://hdl.handle.net/20.500.14454/3033We 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.eng© The Author(s) 2023Convex geometrySensor designShape optimizationjournal article2025-06-12