The University of Southampton
University of Southampton Institutional Repository

A semismooth newton method for the nearest Euclidean distance matrix problem

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.
0895-4798
67-93
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
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), 67-93. (doi:10.1137/110849523).

Record type: Article

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
Download (444kB)

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
ORCID for Houduo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 31 Jan 2013 14:03
Last modified: 09 Jan 2022 03:17

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×