A quadratically convergent Newton method for the nearest correlation matrix problem
A quadratically convergent Newton method for the nearest correlation matrix problem
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.
correlation matrix, semismooth matrix equation, newton method, quadratic convergence
360-385
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Sun, Defeng
48acb796-0417-4d19-8be8-1739d44e50b0
April 2006
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Sun, Defeng
48acb796-0417-4d19-8be8-1739d44e50b0
Qi, Houduo and Sun, Defeng
(2006)
A quadratically convergent Newton method for the nearest correlation matrix problem.
SIAM Journal on Matrix Analysis and Applications, 28 (2), .
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.
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Published date: April 2006
Keywords:
correlation matrix, semismooth matrix equation, newton method, quadratic convergence
Organisations:
Operational Research
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Local EPrints ID: 43246
URI: http://eprints.soton.ac.uk/id/eprint/43246
ISSN: 0895-4798
PURE UUID: 52289fbf-097d-40f6-aa0d-523e83a8deb9
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Date deposited: 13 Jul 2007
Last modified: 16 Mar 2024 03:41
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Author:
Defeng Sun
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