Modern Methods in Nonlinear Optimizartion: Finite Element Methods for PDE-Constrained Optimal Control Problems [MA4503/MA4505]

The description of the modules (4503) and (4505) can be found here and here, respectively.
Many areas of science and engineering involve optimal control of processes that are modelled through partial differential equations. In this course we will cover theoretical foundations and numerical methods for solving such optimization problems. The discussed methods can be used for example for optimally controlling heating-up or cooling-down processes, fluids, or chemical reactions.
We discuss different discretization concepts carefully taking into account the difference between discretization of a single equation and the discretization of an optimization problem. We derive a priori error estimates for different situations including problems with inequality constraints as well as problems governed by semilinear PDEs. Moreover, we discuss a posteriori error estimates and adaptive mesh refinement algorithms for PDE-constrained optimization. Last but not least, we give an overview of current research topics in this area.
Lectures: Prof. Dr. Boris Vexler, Room: 03.06.035, E-Mail:
Exercises: Dr. Johannes Pfefferer, Room: 03.06.036, E-Mail:
Lecture: Monday, 14:15 - 15:45, Room 00.07.014
Exercises: Group 1: Tuesday, 16:00 - 17:30, Room 03.06.011
on April 19, May 3, May 24, May 31, June 21, June 28 and July 12
Group 2: Wednesday, 16:00 - 17:30, Room 02.08.020
on April 20, May 4, May 25, June 1, June 22, June 29 and July 13
The exam will take place on 19th of July, 10:30 am to 11:30 am in Interimshörsaal 2.
The inspection of the first exam will take place on 26th of July, 14:00 pm to 15:00 pm in room 03.06.011.
The repeat exam will take place on 28th of September, 10:30 am to 11:30 am in MI Hörsaal 3.
The inspection of the repeat exam will take place on 13th of October, 11:00 am to 12 noon in room 03.06.036.
You may bring one sheet of A4 size paper with hand-written notes (two-sided), but no other resources such as phones, calculators, books, and the like. Make sure to bring your German national ID card/passport and student ID card.
Additional course on practical aspects
Please note that during the semester break we offer an additional lab course for everyone interested in the practical aspects of optimiziation with PDEs.
Lecture notes
Lecture notes are available on Moodle.
Problem sheets
Problem sheets are available on Moodle
• S. C. Brenner, L. R. Scott: "The Mathematical Theory of Finite Element Methods", Texts in Applied Mathematics, volume 15, Springer, 2008.
• L. C. Evans: "Partial Differential Equations: Second Edition", Graduate Studies in Mathematics, volume 19, AMS, 2010.
• Ch. Grossmann, H.-G. Roos, M. Stynes: "Numerical Treatment of Partial Differential Equations", Universitext, Springer, 2007.
• M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich: "Optimization with PDE constraints", Mathematical Modelling: Theory and Applications, volume 23, Springer, 2009.
• R. Rannacher: "Numerische Mathematik 2 Pfeil", Lecture notes, Institut für angewandte Mathematik, Universität Heidelberg, 2008.
• F. Tröltzsch: "Optimal Control of Partial Differential Equations: Theory, Methods and Applications", Graduate Studies in Mathematics, volume 112, AMS, 2010.
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