A semismooth newton method for the nearest Euclidean distance matrix problem
A semismooth newton method for the nearest Euclidean distance matrix problem
The Nearest Euclidean distance matrix problem (NEDM) is a fundamental
computational problem in applications such as
multidimensional scaling and molecular
conformation from nuclear magnetic resonance data in computational chemistry.
Especially in the latter application, the problem is often large scale with the number of
atoms ranging from a few hundreds to a few thousands.
In this paper, we introduce a
semismooth Newton method that solves the dual problem of (NEDM). We prove that the
method is quadratically convergent.
We then present an application of the Newton method to NEDM with $H$-weights.
We demonstrate the superior performance of the Newton method over existing methods
including the latest quadratic semi-definite programming solver.
This research also opens a new avenue towards efficient solution methods for the molecular
embedding problem.
67-93
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
2013
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Houduo
(2013)
A semismooth newton method for the nearest Euclidean distance matrix problem.
SIAM Journal on Matrix Analysis and Applications, 34 (1), .
(doi:10.1137/110849523).
Abstract
The Nearest Euclidean distance matrix problem (NEDM) is a fundamental
computational problem in applications such as
multidimensional scaling and molecular
conformation from nuclear magnetic resonance data in computational chemistry.
Especially in the latter application, the problem is often large scale with the number of
atoms ranging from a few hundreds to a few thousands.
In this paper, we introduce a
semismooth Newton method that solves the dual problem of (NEDM). We prove that the
method is quadratically convergent.
We then present an application of the Newton method to NEDM with $H$-weights.
We demonstrate the superior performance of the Newton method over existing methods
including the latest quadratic semi-definite programming solver.
This research also opens a new avenue towards efficient solution methods for the molecular
embedding problem.
Text
084952RRRR.pdf
- Author's Original
More information
Published date: 2013
Organisations:
Operational Research
Identifiers
Local EPrints ID: 347784
URI: http://eprints.soton.ac.uk/id/eprint/347784
ISSN: 0895-4798
PURE UUID: 8b01a56d-6674-4036-9d37-024ad60a9b80
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Date deposited: 31 Jan 2013 14:03
Last modified: 15 Mar 2024 03:21
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