Error forgetting of Bregman iteration

Published in Journal of Scientific Computing.


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 w^k denote the error introduced by early stopping a subproblem solver at iteration k. We show that if all w^k 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.

Bregman error forgetting demo 


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

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