University of Toronto
                  PDE/Applied Math/Analysis Seminar
                    Wednesday 18 October, 3:10-4pm
		       Fields' Institute Library


SPEAKER:  Peter Maass (Bremen)

TITLE:    Inverse Problems with Sparsity Constraints

ABSTRACT: The talk will start with a a short description of the Bremen 
          Center for Scientific Computing and Applications (BreSCA) and 
          its mathematical department ZeTeM (Center for Industrial 
          Mathematics).  We will then address inverse problems, which 
          arise in monitoring production processes from assembling 
          aero-turbines to operating classical linear guideways.  Such 
          problems are mathematically modeled as a parameter 
          identification problem for a system of differential 
          equations.

          The second part of the talk will be concerned with the 
          convergence properties of a generalized gradient method for   
          the minimization problem

                          min  F(u) + Phi (u) ,

          where F is assumed to be differentiable but not convex and
          Phi is assumed to be convex but not differentiable. Hence 
          the overall functional is neither convex nor differentiable.

          This type of functionals includes the case of Tikhonov 
          regularization for non-linear inverse problems as a 
          special case:

                         min ||A(u) - g|| + alpha |u| ,

          where |u| denotes e.g. a sparsity constraint or a non-
          differentiable Besov norm.

          We return to the application of inverse problems in the third 
          and last part of the talk. We will primarily address the results 
          of our cooperation with RollsRoyce AeroEngines and Siemens 
          Large Drives on monitoring turbines.



------------------------------------------------------------------
University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2006-2007 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Robert McCann		mccann@ math.toronto.edu
------------------------------------------------------------------