University of Alberta FAST GRADIENT ALGORITHMS FOR STRUCTURED SPARSITY

and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatever without the author’s prior written permission. To my grandpa. Many machine learning problems can be formulated under the composite minimization framework which usually involves a smooth loss function and a nonsmooth regularizer. A lot of algorithms have thus been proposed and the main focus has been on first order gradient methods, due to their appli-cability in very large scale application domains. A common requirement of many of these popular gradient algorithms is the access to the proximal map of the regularizer, which unfortunately may not be easily computable in scenarios such as structured sparsity. In this thesis we first identify condi-tions under which the proximal map of a sum of functions is simply the composition of the proxima