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math.OC2024
Two-norm discrepancy and convergence of the stochastic gradient method with application to shape optimization
Marc Dambrine, Caroline Geiersbach, Helmut Harbrecht
The present article is dedicated to proving convergence of the stochastic gradient method in case of random shape optimization problems. To that end, we consider Bernoulli's exteri…
math.OC2024
On the penalization by the perimeter in shape optimization applied to Dirichlet inverse obstacle problem
Fabien Caubet, Marc Dambrine, Jérémi Dardé
This paper is devoted to the understanding of regularisation process in the shape optimization approach to the so-called Dirichlet inverse obstacle problem for elliptic operators.…