– M. El Gheche (LIGM) : Proximal methods for convex minimization of ?-divergences

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Date(s) - 10 octobre 2014

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Proximal methods for convex minimization of ?-divergences by M. Gueche\n\n?-divergences introduced by Csiszar in 1963 constitutes a useful class of similarity measures, especially in information theory. These divergences correspond to multivariate functions, which are not separable sums of functions of one real variable. We investigate their use as cost functions in possibly nonsmooth large dimensional convex optimization problems like those encountered in imaging and machine learn- ing. After showing how to compute the corresponding proximity operators in a simple manner, we propose novel primal-dual methods, derived from the theory of monotone operators, leading to efficient proximal algorithms. The flexibility of the proposed approaches stems from the fact that the divergences may be composed with arbitrary linear operators.[