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Article Dans Une Revue Mathematical Programming, Series A Année : 2013

Randomized first order algorithms with applications to ℓ 1-minimization

Résumé

In this paper we propose randomized first-order algorithms for solving bilinear saddle points problems. Our developments are motivated by the need for sublinear time algorithms to solve large-scale parametric bilinear saddle point problems where cheap online assessment of the solution quality is crucial. We present the theoretical efficiency estimates of our algorithms and discuss a number of applications, primarily to the problem of ℓ 1 minimization arising in sparsity-oriented signal processing. We demonstrate, both theoretically and by numerical examples, that when seeking for medium-accuracy solutions of large-scale ℓ 1 minimization problems, our randomized algorithms outperform significantly (and progressively as the sizes of the problem grow) the state-of-the art deterministic methods.

Dates et versions

hal-00976864 , version 1 (10-04-2014)

Identifiants

Citer

Anatoli B. Juditsky, Fatma Kilinc Karzan, Arkadii S. Nemirovski. Randomized first order algorithms with applications to ℓ 1-minimization. Mathematical Programming, Series A, 2013, 142 (1-2), pp.269-310. ⟨10.1007/s10107-012-0575-2⟩. ⟨hal-00976864⟩
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