the Institute for Theoretical and Engineering Science
Department of Mathematics

University of Houston

Scientific Computing Seminar

Professor Michael Ulbrich
Munich Univ. of Technology

Primal-dual interior-point methods for optimization
problems with PDE and control constraints

Thursday, Nov. 2, 2006
3:00 PM- 4:00 PM
Room 634 S&R1

Abstract:

Primal-dual interior-point methods have proven to be very efficient in the context of large scale nonlinear programming. In this talk, we present a convergence analysis of a primal-dual interior-point method for PDE-constrained optimization in an appropriate function space setting. Considered are optimal control problems with control constraints in $L^p$. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the $L^\infty$-setting is analyzed, but also a more involved $L^q$-analysis, $q<\infty$, is presented. In $L^\infty$, the set of feasible controls contains interior points and the Fréchet differentiability of the perturbed optimality system can be shown. In the $L^q$-setting, which is highly relevant for PDE-constrained optimization, these nice properties are no longer available. Nevertheless, using refined techniques, a convergence analysis can be carried out. In particular, two-norm techniques and a smoothing step are required. Numerical results are presented.

This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.