Equivalence of a Generalized Conditional Gradient Method and the Method of Surrogate Functionals
نویسندگان
چکیده
This article combines techniques from two fields of applied mathematics: optimization theory and inverse problems. We investigate the equivalence of the classical conditional gradient method and the surrogate method, which has been recently proposed for solving inverse problems. The method of surrogate functionals 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 method of surrogate functionals.
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