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arXiv · 1409.2617

Large-scale randomized-coordinate descent methods with non-separable linear constraints

Sashank Reddi·Ahmed Hefny·Carlton Downey·Avinava Dubey·Suvrit Sra
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Abstract

We develop randomized (block) coordinate descent (CD) methods for linearly constrained convex optimization. Unlike most CD methods, we do not assume the constraints to be separable, but let them be coupled linearly. To our knowledge, ours is the first CD method that allows linear coupling constraints, without making the global iteration complexity have an exponential dependence on the number of constraints. We present algorithms and analysis for four key problem scenarios: (i) smooth; (ii) smooth + nonsmooth separable; (iii) asynchronous parallel; and (iv) stochastic. We illustrate empirical behavior of our algorithms by simulation experiments.

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Sashank Reddi, Ahmed Hefny, Carlton Downey, Avinava Dubey, Suvrit Sra. 2014-09-09. Large-scale randomized-coordinate descent methods with non-separable linear constraints. https://arxiv.org/abs/1409.2617

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