- Approximation of rank function and its application to the nearest low-rank correlation matrix shujun Bi(beamilan163.com) shaohua Pan(shhpanscut.edu.cn) Abstract: 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. Keywords: rank optimization problem; approximation; convex relaxation; nearest low-rank correlation matrix; semismooth Newton method Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Category 3: Applications -- Science and Engineering Citation: Department of Mathematics, South China University of Technology, Guangzhou City, China, July 10, 2011 Download: [PDF]Entry Submitted: 07/10/2011Entry Accepted: 07/11/2011Entry Last Modified: 07/10/2011Modify/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.