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Chapitre D'ouvrage Année : 2010

First Order Methods for Nonsmooth Convex Large-Scale Optimization, II: Utilizing Problem's Structure

Résumé

We present several state-of-the-art First Order methods for "well-structured" large-scale nonsmooth convex programs. In contrast to their "black-boxoriented" prototypes considered in Chapter 1, the methods in question utilize the problem structure in order to convert the original nonsmooth minimization problem into a saddle point problem with smooth convex-concave cost function. This reformulation allows to accelerate signi cantly the solution process. As in Chapter 1, our emphasis is on methods which, under favorable circumstances, exhibit (nearly) dimension-independent convergence rate. Along with investigating the general "well-structured" situation, we outline possibilities to further accelerate First Order methods by randomization.
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Dates et versions

hal-00981864 , version 1 (23-04-2014)

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  • HAL Id : hal-00981864 , version 1

Citer

Anatoli B. Juditsky, Arkadii S. Nemirovski. First Order Methods for Nonsmooth Convex Large-Scale Optimization, II: Utilizing Problem's Structure. Suvrit Sra, Sebastian Nowozin,Stephen J. Wright. Optimization for Machine Learning, MIT Press, pp.29-63, 2010. ⟨hal-00981864⟩
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