- Accelerated Linearized Bregman Method Bo Huang(bh2359columbia.edu) Shiqian Ma(sm2756columbia.edu) Donald Goldfarb(goldfarbcolumbia.edu) Abstract: In this paper, we propose and analyze an accelerated linearized Bregman (ALB) method for solving the basis pursuit and related sparse optimization problems. This accelerated algorithm is based on the fact that the linearized Bregman (LB) algorithm 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. Keywords: Convex Optimization, Linearized Bregman Method, Accelerated Linearized Bregman Method, Compressed Sensing, Basis Pursuit, Matrix Completion Category 1: Convex and Nonsmooth Optimization Citation: Technical Report, Columbia University, June 2011 Download: [PDF]Entry Submitted: 06/27/2011Entry Accepted: 06/28/2011Entry Last Modified: 06/27/2011Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.