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

We develop randomized block coordinate descent (CD) methods for linearly constrained convex optimization. Unlike other large-scale CD methods, we do not assume the constraints to be separable, but allow 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 theoretical analysis for four key (convex) scenarios: (i) smooth; (ii) smooth + separable nonsmooth; (iii) asynchronous parallel; and (iv) stochastic. We discuss some architectural details of our methods and present preliminary results to illustrate the behavior of our algorithms.