Computational Optimization and Applications

, Volume 70, Issue 2, pp 351–394 | Cite as

A flexible coordinate descent method

  • Kimon Fountoulakis
  • Rachael TappendenEmail author


We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Flexible Coordinate Descent (FCD). At each iteration of FCD, a block of coordinates is sampled randomly, a quadratic model is formed about that block and the model is minimized approximately/inexactly to determine the search direction. An inexpensive line search is then employed to ensure a monotonic decrease in the objective function and acceptance of large step sizes. We present several high probability iteration complexity results to show that convergence of FCD is guaranteed theoretically. Finally, we present numerical results on large-scale problems to demonstrate the practical performance of the method.


Large scale optimization Second-order methods Curvature information Block coordinate descent Nonsmooth problems Iteration complexity Randomized 

Mathematics Subject Classification

49M15 49M37 65K05 90C06 90C25 90C53 



We would like to thank the anonymous reviewers for their helpful comments and suggestions, which led to improvements of an earlier version of this paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics, International Computer Science InstituteUniversity of California BerkeleyBerkeleyUSA
  2. 2.School of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand

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