Biannual Report - Fachbereich Mathematik - Technische Universität ...

of actuators, at which modern techniques of robust optimization are applied and extended.
In particular we choose a worst-case approach to incorporate the existing uncertainty into
our optimization model. This leads to a computationally intractable problem formulation
since we consider nonlinear nonconvex objective functions and further employ complex
PDE constraints in order to model the mechanical behaviour of the considered structures.
Hence, this so-called robust counterpart is approximated by means of a second order Taylor
expansion which is solved by an efficient SQP method.
Partner: Collaborative Research Centre (SFB) 805: “Control of uncertainty of load carrying
systems in mechanical engineering”; Speaker H. Hanselka (Department of Mechanical
Engineering, TU Darmstadt)
Support: German Research Foundation (DFG)
Contact: A. Sichau, S. Ulbrich
References
[1] A. Sichau and S. Ulbrich. A Second Order Approximation Technique for Robust Shape Optimization.
Applied Mechanics and Materials, 104:1–40, 2011.
Project: SPEAR – Sparse Exact and Approximate Recovery
The research project “SPEAR – Sparse Exact and Approximate Recovery” deals with the
problem to recover a sparse solution of an underdetermined linear (equality) system. This
topic has many applications and is a very active research area. It is located at the border
between analysis and combinatorial optimization. The main goal of our project is to
obtain a better understanding of the conditions under which (efficiently) finding such a
sparse solution i.e., recovery is possible. Our project is characterized by both theoretical
and computational aspects as well as the interplay of continuous and discrete methods.
The SPEAR project is a collaboration of the Research Group Optimization at the TU Darmstadt
(since 2012, previously: Institute for Mathematical Optimization at the TU Braunschweig)
and the Institute for Analysis and Algebra at the TU Braunschweig. The project
is funded by a DFG research grant. Designated project period: 2011–2014.
Partner: D. A. Lorenz and C. Kruschel, TU Braunschweig
Support: German Research Foundation (DFG)
Contact: M. Pfetsch, A. Tillmann
References
[1] D. A. Lorenz, M. E. Pfetsch, and A. M. Tillmann. An infeasible-point subgradient method using
adaptive approximate projections. Preprint, TU Darmstadt, TU Braunschweig, 2012.
[2] D. A. Lorenz, M. E. Pfetsch, and A. M. Tillmann. Solving basis pursuit: Subgradient algorithm,
heuristic optimality check, and solver comparison. Preprint, TU Darmstadt, TU Braunschweig,
2012.
[3] M. E. Pfetsch and A. M. Tillmann. The computational complexity of the restricted isometry
property, the nullspace property, and related concepts in compressed sensing. Preprint, TU
Darmstadt, 2012.
[4] S. Wenger, M. Ament, S. Guthe, D. A. Lorenz, A. M. Tillmann, D. Weiskopf, and M. Magnor. Visualization
of astronomical nebulae via distributed multi-gpu compressed sensing tomography.
IEEE Transactions on Visualization and Computer Graphics, 18:2188–2197, 2012.
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