fast adaptive shrinkage/thresholding algorithm

FASTA (Fast Adaptive Shrinkage/Thresholding Algorithm) is an efficient, easy-to-use implementation of the Forward-Backward Splitting (FBS) method for minimizing compound objective functions. Many variations on FBS are available in FASTA, including the popular accelerated variant FISTA (Beck and Teboulle ’09), the adaptive stepsize rule SpaRSA (Wright, Nowak, Figueiredo ’09), and other variants described in the review A Field Guide to Forward-Backward Splitting with a FASTA Implementation.

The following files are available for download:

What can FASTA solve?
FASTA targets problems of the form
minimize     f(Ax)+g(x)
where  A is a linear operator, f  is a differentiable function, and g is a “simple” (but possibly non-smooth) function. Problems of this form including sparse least-squares (basis-pursuit), lasso, total-variation denoising, matrix completion, and many more. The FASTA implementation is incredibly flexible; users can solve almost anything by providing their own f, g, and A.  However, for users that want quick out-of-the-box solutions, simple customized solvers are provided for the following problems. See the FASTA user’s manual for details.

solvable problems

About the Authors
Fasta was developed by:
Tom Goldstein - University of Maryland
   Christoph Studer - Cornell University
   Richard Baraniuk - Rice University

How to cite FASTA
If you find that FASTA has contributed to your published work, please include the following citations:

  Author = {Goldstein, Tom and Studer, Christoph and Baraniuk, Richard},
  Title = {A Field Guide to Forward-Backward Splitting with a {FASTA} Implementation},
  year = {2014},
  journal = {arXiv eprint},
  volume = {abs/1411.3406},
  url = {},
  ee = {}

Author = {Goldstein, Tom and Studer, Christoph and Baraniuk, Richard},
  title = {{FASTA}:  A Generalized Implementation of Forward-Backward Splitting},
  note = {},
  month = {January},
  year = {2015}