A generalized conditional gradient method and its connection to an iterative shrinkage method

Authors:
Kristian Bredies;Dirk A. Lorenz;Peter Maass
Affiliations:
Fachbereich 03, Universität Bremen, Bremen, Germany 28334;Electrical Engineering Department, Technion--Israel Institute of Technology, Haifa, Israel 32000;Fachbereich 03, Universität Bremen, Bremen, Germany 28334
Venue:
Computational Optimization and Applications
Year:
2009

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Abstract

This article combines techniques from two fields of applied mathematics: optimization theory and inverse problems. We investigate a generalized conditional gradient method and its connection to an iterative shrinkage method, which has been recently proposed for solving inverse problems.The iterative shrinkage method aims at the solution of non-quadratic minimization problems where the solution is expected to have a sparse representation in a known basis. We show that it can be interpreted as a generalized conditional gradient method. We prove the convergence of this generalized method for general class of functionals, which includes non-convex functionals. This also gives a deeper understanding of the iterative shrinkage method.