On convex sets that minimize the average distance

DOI10.1051/COCV/2011190zbMath1259.49065OpenAlexW2142774279MaRDI QIDQ4910997

Edoardo Mainini, Antoine Lemenant

Publication date: 13 March 2013

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/cocv/2011190

zbMATH Keywords

optimality conditionsshape optimizationconvex analysis\(\Gamma\)-convergencedistance functionalsecond order variation

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

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The average-distance problem with an Euler elastica penalization ⋮ The Average Distance Problem with Perimeter-to-Area Ratio Penalization ⋮ Optimal design of sensors via geometric criteria ⋮ A presentation of the average distance minimizing problem ⋮ Regularity and singularities of optimal convex shapes in the plane

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