On the Convergence of the Iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm”

A. Chambolle () and Ch. Dossal ()
Additional contact information
A. Chambolle: CMAP, Ecole Polytechnique, CNRS
Ch. Dossal: IMB, Univ. Bordeaux 1, CNRS

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 3, No 14, 968-982

Abstract: Abstract We discuss here the convergence of the iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm,” which is an algorithm proposed by Beck and Teboulle for minimizing the sum of two convex, lower-semicontinuous, and proper functions (defined in a Euclidean or Hilbert space), such that one is differentiable with Lipschitz gradient, and the proximity operator of the second is easy to compute. It builds a sequence of iterates for which the objective is controlled, up to a (nearly optimal) constant, by the inverse of the square of the iteration number. However, the convergence of the iterates themselves is not known. We show here that with a small modification, we can ensure the same upper bound for the decay of the energy, as well as the convergence of the iterates to a minimizer.

Keywords: Optimization; First-order schemes; Convergence; Forward backward splitting; Inertial algorithms; 65Y20; 65B99; 90C25 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-015-0746-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:166:y:2015:i:3:d:10.1007_s10957-015-0746-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-015-0746-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().