Invited Session Fri.3.MA 144

Friday, 15:15 - 16:45 h, Room: MA 144

Cluster 22: Stochastic optimization [...]

PDE constrained stochastic optimization


Chair: RĂ¼diger Schultz



Friday, 15:15 - 15:40 h, Room: MA 144, Talk 1

RĂ¼diger Schultz
Shape optimization under uncertainty via stochastic optimization

Coauthors: Sergio Conti, Harald Held, Martin Pach, Martin Rumpf


Shape optimization with linearized elasticity and stochastic loading is put into the framework of two-stage stochastic programming. Principal model set ups, both risk neutral and risk averse, are discussed. Outlines of solution procedures and some computational experiments complete the talk.



Friday, 15:45 - 16:10 h, Room: MA 144, Talk 2

Benedict Geihe
A two-scale approach for risk averse shape optimization


We investigate macroscopic geometries with underlying periodic lattices of fine scale structures. These details are supposed to be parametrized via a finite number of parameters over which we optimize. Risk averse stochastic cost functionals are taken into account. We employ a two-scale approach based on boundary elements for the elastic problem on the microscale and finite elements on the macroscale.



Friday, 16:15 - 16:40 h, Room: MA 144, Talk 3

Tony Huschto
Solving stochastic optimal control problems by a polynomial chaos approach

Coauthor: Sebastian Sager


In optimal control problems driven by stochastic differential equations, the detection of optimal (Markovian) decision rules is a very challenging task. Explicit solutions can be found in only very few cases by considering the corresponding Hamilton-Jacobi-Bellman equation. Thus numerical methods, e.g., based on Markov chains, have attracted great interest.
In this contribution, we introduce a new methodology for solving continuous finite-horizon stochastic optimal control problems. We utilize ideas for approximating stochastic differential equations within the framework of Polynomial Chaos and expand this to reformulate stochastic optimal control problems directly into deterministic ones. This allows us to use Bock's direct multiple shooting method, a state of the art simultaneous method to solve optimization and simulation tasks at the same time. We implement different approaches to preserve the feedback character of the optimal decision rules. Numerical examples illustrate this new methodology and show the validity of the developed reformulations.


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