We propose and analyze an accelerated linearized Bregman (ALB) method for solving the basis pursuit and related sparse optimization problems. Our algorithm is based on the fact that the linearized Bregman (LB) algorithm first proposed by Stanley Osher and his collaborators is equivalent to a gradient descent method applied to a certain dual formulation. We show that the LB method requires O(1/epsilon) iterations to obtain an epsilon-optimal solution and the ALB algorithm reduces this iteration complexity to O(1/\sqrt epsilon)) while requiring almost the same computational effort on each iteration. Numerical results on compressed sensing and matrix completion problems are presented that demonstrate that the ALB method can be significantly faster than the LB method. This is joint work with Bo Huang and Shiqian Ma
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