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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2015

Shape optimization for quadratic functionals and states with random right-hand sides

Résumé

In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation where the state function depends linearly on a random input parameter. This framework covers important objectives such as tracking-type functionals for elliptic second order partial differential equations and the compliance in linear elasticity. We show that the robust objective and its gradient are completely and explicitly determined by low-order moments of the random input. We then derive a cheap, deterministic algorithm to minimize this objective and present model cases in structural optimization.
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Dates et versions

hal-01143319 , version 1 (28-05-2015)

Identifiants

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Marc Dambrine, Charles Dapogny, Helmut Harbrecht. Shape optimization for quadratic functionals and states with random right-hand sides. SIAM Journal on Control and Optimization, 2015, 53 (5), pp.2725-3317. ⟨10.1137/15M1017041⟩. ⟨hal-01143319⟩
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