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Acceleration of alternating minimisations for quadratic + nonsmooth problems

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We consider Dykstra-like algorithms for solving the proximity operator of the sum of two simple convex functions. We show that this shares common features with forward-backward descent schemes, and this allows to implement standard acceleration techniques (a la Nesterov or Beck and Teboulle’s FISTA ) to improve the theoretical upper bound on the convergence rate. As an application we show how to implement efficient parallel techniques to compute the proximity operator of the total variation (that is, solve the “Rudin-Osher-Fatemi” minimisation problem).

This talk is part of the Applied and Computational Analysis series.

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