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

Shujun Bi (), Le Han () and Shaohua Pan ()

Journal of Global Optimization, 2013, vol. 57, issue 4, 1113-1137

Abstract: The rank function rank(.) 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(.), 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 results indicate that this convex relaxation method is comparable with the sequential semismooth Newton method (Li and Qi in SIAM J Optim 21:1641–1666, 2011 ) and the majorized penalty approach (Gao and Sun, 2010 ) in terms of the quality of solutions. Copyright Springer Science+Business Media New York 2013

Keywords: Rank optimization problem; Approximation; Convex relaxation; Nearest low-rank correlation matrix; Semismooth Newton method (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-0007-0

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