Authors
Antonin Chambolle, Ch Dossal
Publication date
2015/9
Journal
Journal of Optimization theory and Applications
Volume
166
Pages
968-982
Publisher
Springer US
Description
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.
Scholar articles
A Chambolle, C Dossal - Journal of Optimization theory and Applications, 2015
A Chambolle, CH Dossal - Journal of Optimization Theory and Applications, 2015
A Chambolle, CH Dossal - 2014
A Chambolle, CH Dossal - 2014