Invited Session Wed.3.MA 415

Wednesday, 15:15 - 16:45 h, Room: MA 415

Cluster 19: PDE-constrained optimization & multi-level/multi-grid methods [...]

Optimization applications in industry V


Chair: Dietmar Hömberg



Wednesday, 15:15 - 15:40 h, Room: MA 415, Talk 1

Arnd Roesch
Optimal control of a chemotaxis problem

Coauthor: Hendrik Feldhordt


Chemotaxis describes a biological phenomenon of self organization and
pattern forming of cell populations caused by chemical substances. It
can be modelled by a two component reaction diffusion system in which
the equations are coupled by a quasilinear cross-diffusion term. In this
talk, an optimal control problem with Neumann boundary control for the
chemoattractant is considered.
We present results on uniform boundedness of the states, existence of
optimal controls and first order necessary optimality conditons.



Wednesday, 15:45 - 16:10 h, Room: MA 415, Talk 2

Antoine Laurain
A shape and topology optimization method for inverse problems in tomography

Coauthors: Manuel Freiberger, Michael Hintermüller, Andr'e A. Novotny, Hermann Scharfetter


We propose a general shape optimization approach for the
resolution of different inverse problems in tomography. For instance, in the case of Electrical Impedance Tomography (EIT), we reconstruct the electrical conductivity while in the case of Fluorescence Diffuse Optical Tomography (FDOT), the unknown is a fluorophore concentration. These problems are in general severely ill-posed, and a standard cure is to make additional assumptions on the unknowns to regularize the problem. Our approach consists in assuming that the functions to be reconstructed are piecewise constants.
Thanks to this hypothesis, the problem essentially boils down to a shape optimization problem. The sensitivity of a certain cost functional with respect to small perturbations of the shapes of these inclusions is analysed. The algorithm consists in initializing the inclusions using the notion of topological derivative, which measures the variation of the cost functional when a small inclusion is introduced in the domain, then to reconstruct the shape of the inclusions by modifying their boundaries with the help of the so-called shape derivative.



Wednesday, 16:15 - 16:40 h, Room: MA 415, Talk 3

Stephania Hokenmaier
Optimization with discontinuities and approximations in process engineering

Coauthor: Barbara Kaltenbacher


Process simulators are indispensable in the daily work of process engineers. The Engineering Division of The Linde Group, which is one of the world leading companies in planning and building process plants, has been developing the in-house process simulation program OPTISIM\raisebox{.5ex}{®} for the simulation and optimization of chemical processes. Increasing demands on the optimizer concerning problem size, efficiency and robustness, especially with the occurance of discontinuities and the use of approximations during simulation and optimization, lead to a closer look towards new optimization methods. In this context the global convergence of the filter line search of Biegler and Wächter, used in the optimizer IPOPT, was considered under the assumption of perturbed equality constraints and derivatives, which models their approximate evaluation as well as to some extent also the discontinuities. Furthermore some numerical results will be shown.


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