# Shape Optimization Under Uncertainty---A Stochastic Programming Perspective

@article{Conti2008ShapeOU, title={Shape Optimization Under Uncertainty---A Stochastic Programming Perspective}, author={Sergio Conti and Harald Held and Martin Pach and Martin Rumpf and R{\"u}diger Schultz}, journal={SIAM J. Optim.}, year={2008}, volume={19}, pages={1610-1632} }

We present an algorithm for shape optimization under stochastic loading and representative numerical results. Our strategy builds upon a combination of techniques from two-stage stochastic programming and level-set-based shape optimization. In particular, usage of linear elasticity and quadratic objective functions permits us to obtain a computational cost which scales linearly in the number of linearly independent applied forces, which often is much smaller than the number of different…

## 99 Citations

### On Shape Optimization with Stochastic Loadings

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Shape optimization of the fine scale geometry of elastic objects is investigated under stochastic loading. Thus, the object geometry is described via parametrized geometric details placed on a…

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