Approximation of rank function and its application to the nearest low-rank correlation matrix

The rank function $\rank(\cdot)$ is neither continuous nor convex which brings much difficulty to the solution of rank minimization problems. In this paper, we provide a unified framework to construct the approximation functions of $\rank(\cdot)$, and study their favorable properties. Particularly, with two families of approximation functions, we propose a convex relaxation method for the rank minimization problems with positive semidefinite cone constraints, and illustrate its application by computing the nearest low-rank correlation matrix. Numerical comparisons with the convex relaxation method in \cite{LQ09} indicate that our method tends to yield a better local optimal solution.

Citation

Department of Mathematics, South China University of Technology, Guangzhou City, China, July 10, 2011

Article

Download

View Approximation of rank function and its application to the nearest low-rank correlation matrix