Inexact Coordinate Descent: Complexity and Preconditioning

Rachael Tappenden (), Peter Richtárik () and Jacek Gondzio ()
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Rachael Tappenden: The University of Edinburgh
Peter Richtárik: The University of Edinburgh
Jacek Gondzio: The University of Edinburgh

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 1, No 10, 144-176

Abstract: Abstract 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.

Keywords: Inexact methods; Block coordinate descent; Convex optimization; Iteration complexity; Preconditioning; Conjugate gradients; 65F08; 65F10; 65F15; 65Y20; 68Q25; 90C25 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-016-0867-4

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