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Rescaled Pure Greedy Algorithm for Convex Optimization

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 Added by Guergana Petrova
 Publication date 2015
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and research's language is English




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We suggest a new greedy strategy for convex optimization in Banach spaces and prove its convergent rates under a suitable behavior of the modulus of uniform smoothness of the objective function.



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162 - Guergana Petrova 2015
We show that a very simple modification of the Pure Greedy Algorithm for approximating functions by sparse sums from a dictionary in a Hilbert or more generally a Banach space has optimal convergence rates on the class of convex combinations of dictionary elements
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing smooth functions with Lipschitz derivatives of an arbitrary order, as well as for smooth minimax optimization problems. The proposed meta-algorithm is more general than the ones in the literature and allows to obtain better convergence rates and practical performance in several settings.
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