author = {Conti, Sergio and Held, Harald and Pach, Martin and Rumpf, Martin
	and Schultz, R{\"{u}}diger},
  title = {Risk Averse Shape Optimization},
  journal = {SIAM Journal on Control and Optimization},
  year = {2011},
  volume = {49},
  pages = {927--947},
  number = {3},
  abstract = {Risk-averse optimization has attracted much attention in finite-dimensional
	stochastic programming. In this paper, we propose a risk-averse approach
	in the infinite dimensional context of shape optimization. We consider
	elastic materials under stochastic loading. As measures of risk awareness
	we investigate the expected excess and the excess probability. The
	developed numerical algorithm is based on a regularized gradient
	flow acting on an implicit description of the shapes based on level
	sets. We incorporate topological derivatives to allow for topological
	changes in the shape optimization procedure. Numerical results in
	2D demonstrate the impact of the risk-averse modeling on the optimal
	shapes and on the cost distribution over the set of scenarios.},
  doi = {10.1137/090754315},
  pdf = { 1},
  keywords = {SHAPE_OPT}