A novel method for a class of structured low-rank minimizations with equality constraint

作者：Bai, Jianchao; Li, Jicheng^*; Xu, Fengmin; Dai, Pingfan

来源：Journal of Computational and Applied Mathematics, 2018, 330: 475-487.

DOI：10.1016/j.cam.2017.09.021

• Low-rank
• Equality constraint
• Positive semidefinite constraint
• Accelerated augmented Lagrangian method

The positive semidefinite constraint and equality constraint arise widely in matrix optimization problems of different areas including signal/image processing, finance and risk management. In this paper, an inexact accelerated Augmented Lagrangian Method (ALM) relying on a parameter m is designed to solve the structured low-rank minimization with equality constraint, which is more general and flexible than the existing ALM and its variants. We prove a worst-case O(1/k(2)) convergence rate of the new method in terms of the residual of the Lagrangian function, and we analyze that when m is an element of [0, 1) the residual of our method is smaller than that of the traditional accelerated ALM. Compared with several state-of-the-art methods, preliminary numerical experiments on solving the Q-weighted low-rank correlation matrix problem from finance validate the efficiency of the proposed method.

• 出版日期2018-3-1
• 单位西安交通大学; 三明学院