===affil2:
University of Leuven
===firstname:
Dirk
===firstname4:

===firstname3:

===lastname2:
Vandewalle
===lastname:
Abbeloos
===firstname5:

===affil6:

===lastname3:

===email:
dirk.abbeloos@cs.kuleuven.be
===lastname6:

===affil5:

===otherauths:

===lastname4:

===affil4:

===lastname7:

===affil7:

===firstname7:

===postal:
Celestijnenlaan 200A,
3001 Heverlee (Beglium)
===firstname6:

===ABSTRACT:
Optimization problems are locally characterized by the spectrum of the Hessian. By default, this spectrum is not a priori known and very expensive to compute. A classical Fourier analysis yields a sufficient approximation of the spectrum, if boundary conditions are not crucial. This makes this type of analysis useless for boundary control problems, i.e. a class of optimization problems where right-hand sides of the boundary conditions needs to be found in order to minimize an objective. 
In this talk we present a mode analysis based on a half-space domain where the effect of only one boundary condition at a time can be included. The resulting half-space analysis is complementary to the classical Fourier analysis. Both a discrete and continuous version of the analysis exists, yielding invaluable information for designing textbook efficient multigrid methods. We present a complete framework as well as it's application to parabolic boundary control problems. 
===affil3:

===lastname5:

===affilother:

===title:
A HALF-SPACE ANALYSIS FRAMEWORK FOR BOUNDARY CONTROL PROBLEMS 
===firstname2:
Stefan