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arXiv · 1711.03439

Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization

Ahmet Alacaoglu·Quoc Tran-Dinh·Olivier Fercoq·Volkan Cevher
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Abstract

We propose a new randomized coordinate descent method for a convex optimization template with broad applications. Our analysis relies on a novel combination of four ideas applied to the primal-dual gap function: smoothing, acceleration, homotopy, and coordinate descent with non-uniform sampling. As a result, our method features the first convergence rate guarantees among the coordinate descent methods, that are the best-known under a variety of common structure assumptions on the template. We provide numerical evidence to support the theoretical results with a comparison to state-of-the-art algorithms.

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Ahmet Alacaoglu, Quoc Tran-Dinh, Olivier Fercoq, Volkan Cevher. 2017-11-09. Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization. https://arxiv.org/abs/1711.03439

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