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Title: A quadratically convergent newton method for computing the nearest correlation matrix
Authors: Qi, H.
Sun, D. 
Keywords: Correlation matrix
Newton method
Quadratic convergence
Semismooth matrix equation
Issue Date: 2006
Citation: Qi, H., Sun, D. (2006). A quadratically convergent newton method for computing the nearest correlation matrix. SIAM Journal on Matrix Analysis and Applications 28 (2) : 360-385. ScholarBank@NUS Repository.
Abstract: The nearest correlation matrix problem is to find a correlation matrix which is closest to a given symmetric matrix in the Frobenius norm. The well-studied dual approach is to reformulate this problem as an unconstrained continuously differentiable convex optimization problem. Gradient methods and quasi-Newton methods such as BFGS have been used directly to obtain globally convergent methods. Since the objective function in the dual approach is not twice continuously differentiable, these methods converge at best linearly. In this paper, we investigate a Newton-type method for the nearest correlation matrix problem. Based on recent developments on strongly semismooth matrix valued functions, we prove the quadratic convergence of the proposed Newton method. Numerical experiments confirm the fast convergence and the high efficiency of the method. © 2006 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Matrix Analysis and Applications
ISSN: 08954798
DOI: 10.1137/050624509
Appears in Collections:Staff Publications

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