This research project dealt 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 located at the border between analysis and combinatorial optimization. The main goal of the project was to obtain a better understanding of the conditions under which (efficiently) finding such a sparse solution, i.e., recovery, is possible. The project was characterized by both theoretical and computational aspects as well as the interplay of continuous and discrete methods.
This project was a collaboration of the Institute for Analysis and Algebra (Lorenz, Kruschel) and the Institute for Mathematical Optimization (Pfetsch, Tillmann) at TU Braunschweig; the latter group moved to TU Darmstadt in 2011/12, where the project work was continued in the Research Group Optimization.