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

Dambrine, Marc and Dapogny, Charles and Harbrecht, Helmut. (2015) Shape optimization for quadratic functionals and states with random right-hand sides. SIAM journal on control and optimization, Vol. 53, H. 5. pp. 3081-3103.

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Official URL: http://edoc.unibas.ch/dok/A6438726

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We consider shape optimization problems under uncertainties on the input parameters. The presented theory applies to the minimization of the expectation of a quadratic objective for a state function that depends linearly on a random input parameter. It 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 determined by low order moments of the random input. We derive a cheap, deterministic algorithm to minimize this objective and present model cases in structural optimization.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Note:Copyright © 2015, Society for Industrial and Applied Mathematics -- Publication type according to Uni Basel Research Database: Journal article
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Last Modified:31 Dec 2015 10:58
Deposited On:06 Nov 2015 10:21

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