Accelerated Bregman Method for Linearly Constrained - Minimization

作者：Kang Myeongmin; Yun Sangwoon; Woo Hyenkyun; Kang Myungjoo

来源：Journal of Scientific Computing, 2013, 56(3): 515-534.

DOI：10.1007/s10915-013-9686-z

• Bregman iteration
• Accelerated Bregman method
• Compressive sensing
• l(1)-l(2) minimization
• Augmented Lagrangian method

In this paper, we consider the linearly constrained - minimization, and we propose an accelerated Bregman method for solving this minimization problem. The proposed method is based on the extrapolation technique, which is used in accelerated proximal gradient methods proposed by Nesterov and others, and on the equivalence between the Bregman method and the augmented Lagrangian method. A convergence rate of is proved for the proposed method when it is applied to solve a more general linearly constrained nonsmooth convex minimization problem. We numerically test our proposed method on a synthetic problem from compressive sensing. The numerical results confirm that our accelerated Bregman method is faster than the original Bregman method.

• 出版日期2013-9