The elastic net:Stability for sparsity methodsStefan SchifflerThe elastic net: Stability for sparsity methodsvon Stefan SchifflerDissertationzur Erlangung des Grades eines Doktors der Naturwissenschaften– Dr.rer.nat –Vorgelegt im Fachbereich 3 (Mathematik & Informatik)der Universit¨ at Bremenim Februar 2010Datum des Promotionskolloquiums: 24.06.2010Gutachter:Prof. Dr. Peter Maaß (Universit¨ at Bremen)Prof. Dr. Dirk A. Lorenz (Technische Universit¨ at Braunschweig)AcknowledgementI would like to thank Prof. Dr. Peter Maaß for providing the possibility ofwriting this thesis in his pleasant working group as well as the chance towork on several interesting industrial projects, related to my research.Moreover, I like to thank Prof. Dr. Dirk A. Lorenz and Prof. Dr. PeterMaaß for their always helpful supervision and persistent support. Further-more, I like to thank Dr. Theodore Alexandrov, Dr. Christian Bredies, Dr.Bangti Jin, Prof. Dr. Dirk Lorenz and Dennis Trede for fruitful discussions,joint works and helpful suggestions. For careful proofreading and helpfulcomments, I am deeply grateful to Dr. Theodore Alexandrov, Dr. BangtiJin, Sankar Natarajan, Sabine Schiffler and Dennis Trede.Last but not least, I want to thank all my colleagues at the ”Zentrumf¨ur Technomathematik“ for the good time and the pleasant working atmo-sphere.Finally,IacknowledgeBrukerDaltonicsforprovidingimagesanddatasets.