-

 

 

 




Optimization Online





 

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

shujun Bi(beamilan***at***163.com)
shaohua Pan(shhpan***at***scut.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: 07/10/2011
Entry Accepted: 07/11/2011
Entry Last Modified: 07/10/2011

Modify/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
Mathematical Optimization Society