Asset Details
Do you wish to reserve the book?
Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
Do you wish to request the book?
Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
2014
Overview
In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an
-accurate solution with probability at least
in at most
iterations, where
is the number of blocks. This extends recent results of Nesterov (SIAM J Optim 22(2): 341–362, 2012), which cover the smooth case, to composite minimization, while at the same time improving the complexity by the factor of 4 and removing
from the logarithmic term. More importantly, in contrast with the aforementioned work in which the author achieves the results by applying the method to a regularized version of the objective function with an unknown scaling factor, we show that this is not necessary, thus achieving first true iteration complexity bounds. For strongly convex functions the method converges linearly. In the smooth case we also allow for arbitrary probability vectors and non-Euclidean norms. Finally, we demonstrate numerically that the algorithm is able to solve huge-scale
-regularized least squares problems with a billion variables.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
