Abstract
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.
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Research was partly supported by the ONR grant N000140811104 and the NSF grant DMS-0914785 (second and third authors) and the BSF grant 2008302 (third author).
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Juditsky, A., Kılınç Karzan, F. & Nemirovski, A. Randomized first order algorithms with applications to ℓ 1-minimization. Math. Program. 142, 269–310 (2013). https://doi.org/10.1007/s10107-012-0575-2
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DOI: https://doi.org/10.1007/s10107-012-0575-2