A sequential semismooth Newton method for the
nearest low-rank correlation matrix problem
A sequential semismooth Newton method for the
nearest low-rank correlation matrix problem
Based on the well known result that the sum of largest eigenvalues of a symmetric matrix can be represented as a semidefinite programming problem (SDP), we formulate the nearest low-rank correlation matrix problem as a nonconvex SDP and propose a numerical method that solves a sequence of least-square problems. Each of the least-square problems can be solved by a specifically designed semismooth Newton method, which is shown to be quadratically convergent.
The sequential method is guaranteed to produce a stationary point of the nonconvex SDP. Our numerical results demonstrate the high efficiency of the proposed method on large scale problems
1641-1666
Li, Qingna
a189d836-f8f0-407b-9983-0a73bf8a214a
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
2011
Li, Qingna
a189d836-f8f0-407b-9983-0a73bf8a214a
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Li, Qingna and Qi, Houduo
(2011)
A sequential semismooth Newton method for the
nearest low-rank correlation matrix problem.
SIAM Journal on Optimization, 21 (4), .
(doi:10.1137/090771181).
Abstract
Based on the well known result that the sum of largest eigenvalues of a symmetric matrix can be represented as a semidefinite programming problem (SDP), we formulate the nearest low-rank correlation matrix problem as a nonconvex SDP and propose a numerical method that solves a sequence of least-square problems. Each of the least-square problems can be solved by a specifically designed semismooth Newton method, which is shown to be quadratically convergent.
The sequential method is guaranteed to produce a stationary point of the nonconvex SDP. Our numerical results demonstrate the high efficiency of the proposed method on large scale problems
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Published date: 2011
Organisations:
Operational Research
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Local EPrints ID: 198597
URI: http://eprints.soton.ac.uk/id/eprint/198597
ISSN: 1052-6234
PURE UUID: 0e556f6a-8a61-48d9-9bfb-f3e321c0014b
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Date deposited: 05 Oct 2011 10:21
Last modified: 15 Mar 2024 03:21
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Author:
Qingna Li
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