author = {Conti, Sergio and Geihe, Benedict and Rumpf, Martin and Schultz,
  title = {Two-Stage Stochastic Optimization Meets Two-Scale Simulation},
  booktitle = {Trends in PDE Constrained Optimization},
  publisher = {Springer International Publishing},
  year = {2014},
  editor = {Leugering, G\"{u}nter and Benner, Peter and Engell, Sebastian and
	Griewank, Andreas and Harbrecht, Helmut and Hinze, Michael and Rannacher,
	Rolf and Ulbrich, Stefan},
  volume = {165},
  series = {International Series of Numerical Mathematics},
  pages = {193--211},
  abstract = {Risk averse stochastic optimization is investigated in the context
	of elastic shape optimization, allowing for microstructures in the
	admissible shapes. In particular, a two-stage model for shape optimization
	under stochastic loading with risk averse cost functionals is combined
	with a two-scale approach for the simulation of microstructured materials.
	The microstructure is composed of an elastic material with geometrically
	simple perforations located on a regular periodic lattice. Different
	types of microscopic geometries are investigated and compared to
	each other. In addition they are compared to optimal nested laminates,
	known to realize the optimal lower bound of compliance cost functionals.
	We combine this two-scale approach to elastic shapes with a two-stage
	stochastic programming approach to risk averse shape optimization,
	dealing with risk neutral and risk averse cost functionals in the
	presence of stochastic loadings.},
  doi = {10.1007/978-3-319-05083-6_13},
  pdf = { 1},
  isbn = {978-3-319-05082-9},
  keywords = {SHAPE_OPT},
  language = {English},
  url = {}