Inexact Coordinate Descent: Complexity and Preconditioning

Rachael Tappenden*, Peter Richtárik, Jacek Gondzio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


One of the key steps at each iteration of a randomized block coordinate descent method consists in determining the update to a block of variables. Existing algorithms assume that in order to compute the update, a particular subproblem is solved exactly. In this work, we relax this requirement and allow for the subproblem to be solved inexactly, leading to an inexact block coordinate descent method. Our approach incorporates the best known results for exact updates as a special case. Moreover, these theoretical guarantees are complemented by practical considerations: the use of iterative techniques to determine the update and the use of preconditioning for further acceleration.

Original languageEnglish (US)
Pages (from-to)144-176
Number of pages33
JournalJournal of Optimization Theory and Applications
Issue number1
StatePublished - Jul 1 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016, The Author(s).


  • Block coordinate descent
  • Conjugate gradients
  • Convex optimization
  • Inexact methods
  • Iteration complexity
  • Preconditioning

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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