Error forgetting of Bregman iteration

Published in Journal of Scientific Computing.

• Technical report

• Matlab demo

• Old website and slides

Overview

This paper explains why in the Bregman iterative procedure (which is the equivalent to the augmented Lagrangian method), solving subproblems at moderate accuracies (1e-6) can give a solution at nearly the machine precision (1e-15).

Let denote the error introduced by early stopping a subproblem solver at iteration . We show that if all are sufficiently small so that Bregman iteration enters the optimal face, then while on the optimal face, Bregman iteration enjoys an interesting error-forgetting property.

Citation

S. Osher and W. Yin, Error forgetting of Bregman iteration, Journal of Scientific Computing, 54(2), 684-695, 2013.