• 论文 •

### 基于改进的不动点迭代算法的低秩Gram矩阵的恢复

1. 中科院数学与系统科学研究院, 数学机械化重点实验室, 北京 100190
• 收稿日期:2010-10-26 修回日期:1900-01-01 出版日期:2010-11-25 发布日期:2010-11-25

MA Yue. The Minimum-Rank Gram Matrix Completion via Fixed Point Continuation Method[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(11): 1501-1511.

### The Minimum-Rank Gram Matrix Completion via Fixed Point Continuation Method

MA Yue

1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190
• Received:2010-10-26 Revised:1900-01-01 Online:2010-11-25 Published:2010-11-25

The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear norm
minimization. Although the latter can be transformed into a semidefinite
programming problem, which is computationally expensive to solve when the matrices are large. In this paper, we propose a new modified fixed point iterative algorithm for solving the nuclear norm minimization problem and prove the convergence of the algorithm. By using the Barzilai-Borwein technique to accelerate the convergence, we get a fast and robust algorithm, which we call
FPC-BB (Fixed Point Continuation with Barzilai-Borwein Technique).

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