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SUMMARY:Low rank methods for PDE-constrained optimization - Martin Stoll (
 Technische Universität Chemnitz)
DTSTART:20180308T114500Z
DTEND:20180308T123000Z
UID:TALK102049@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Optimization subject to PDE constraints is crucial in many app
 lications . Numerical analysis has contributed a great deal to allow for t
 he efficient solution of these problems and our focus in this talk will be
  on the solution of the large scale linear systems that represent the firs
 t order optimality conditions. We illustrate that these systems\, while be
 ing of very large dimension\, usually contain a lot of mathematical struct
 ure. In particular\, we focus on  low-rank methods that utilize the Kronec
 ker product structure of the system matrices. These methods allow the solu
 tion of a time-dependent problem with the storage requirements of a small 
 multiple of the steady problem. Furthermore\, this technique can be used t
 o tackle the added dimensionality when we consider optimization problems s
 ubject to PDEs with uncertain coefficients. The stochastic Galerkin FEM te
 chnique leads to a vast dimensional system that would be infeasible on any
  computer but using low-rank techniques this can be solved on a standard l
 aptop computer.
LOCATION:Seminar Room 1\, Newton Institute
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