Accelerating block coordinate descent methods with identification strategies

Ronaldo Lopes, Sandra Santos, and Paulo J. S. Silva. Computational Optimization and Applications, 2019.

Abstract

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This work is about active set identification strategies aimed at accelerating block-coordinate descent methods (BCDM) applied to large-scale problems. We start by devising an identification function tailored for bound-constrained composite minimization together with an associated version of the BCDM, called Active BCDM, that is also globally convergent. The identification function gives rise to an efficient practical strategy for Lasso and ℓ1-regularized logistic regression. The computational performance of Active BCDM is contextualized using comparative sets of experiments that are based on the solution of problems with data from deterministic instances from the literature. These results have been compared with those of well-established and state-of-the-art methods that are particularly suited for the classes of applications under consideration. Active BCDM has proved useful in achieving fast results due to its identification strategy. Besides that, an extra second-order step was used, with favorable cost-benefit.