On the Convergence Rate of Dual Ascent Methods for Linearly Constrained Convex Minimization

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Abstract
We analyze the rate of convergence of certain dual ascent methods for the problem of minimizing a strictly convex essentially smooth function subject to linear constraints. Included in our study are dual coordinate ascent methods and dual gradient methods. We show that, under mild assumptions on the problem, these methods attain a linear rate of convergence. Our proof is based on estimating the distance from a feasible dual solution to the optimal dual solution set by the norm of a certain residual.