FASTA: A Generalized Implementation of Forward-Backward Splitting

where | · | denotes the `1 norm, ‖·‖ denotes the `2 norm, A is a matrix, b is a vector, and μ is a scalar parameter. This problem is of the form (1) with g(z) = μ|z|, and f(z) = 12‖z− b‖ . More generally, any problem of the form (1) can be solved by FASTA, provided the user can provide function handles to f, g, A and A . The solver FASTA contains numerous enhancements of FBS to improve convergence speed and usability. These include adaptive stepsize choice, acceleration (i.e., of the type used by the solver FISTA), backtracking line search, and numerous automated stopping conditions, and many other improvements reviews in the article A Field Guide to Forward-Backward Splitting with a FASTA Implementation.