The University of Southampton
University of Southampton Institutional Repository

Numerical methods for constrained Euclidean distance matrix optimization

Numerical methods for constrained Euclidean distance matrix optimization
Numerical methods for constrained Euclidean distance matrix optimization
This thesis is an accumulation of work regarding a class of constrained Euclidean Distance Matrix (EDM) based optimization models and corresponding numerical approaches. EDM-based optimization is powerful for processing distance information which appears in diverse applications arising from a wide range of fields, from which the motivation for this work comes. Those problems usually involve minimizing the error of distance measurements as well as satisfying some Euclidean distance constraints, which may present enormous challenge to the existing algorithms. In this thesis, we focus on problems with two different types of constraints. The first one consists of spherical constraints which comes from spherical data representation and the other one has a large number of bound constraints which comes from wireless sensor network localization.

For spherical data representation, we reformulate the problem as an Euclidean distance matrix optimization problem with a low rank constraint. We then propose an iterative algorithm that uses a quadratically convergent Newton-CG method at its each step. We study fundamental issues including constraint nondegeneracy and the nonsingularity of generalized Jacobian that ensure the quadratic convergence of the Newton method. We use some classic examples from the spherical multidimensional scaling to demonstrate the flexibility of the algorithm in incorporating various constraints.

For wireless sensor network localization, we set up a convex optimization model using EDM which integrates connectivity information as lower and upper bounds on the elements of EDM, resulting in an EDM-based localization scheme that possesses both efficiency and robustness in dealing with flip ambiguity under the presence of high level of noises in distance measurements and irregular topology of the concerning network of moderate size.

To localize a large-scale network efficiently, we propose a patching-stitching localization scheme which divides the network into several sub-networks, localizes each sub-network separately and stitching all the sub-networks together to get the recovered network. Mechanism for separating the network is discussed. EDM-based optimization model can be extended to add more constraints, resulting in a flexible localization scheme for various kinds of applications. Numerical results show that the proposed algorithm is promising.
Bai, Shuanghua
91e9bb33-da7d-4316-beb7-1e774032c2ba
Bai, Shuanghua
91e9bb33-da7d-4316-beb7-1e774032c2ba
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Nguyen, Tri-Dung
a6aa7081-6bf7-488a-b72f-510328958a8e
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5

Bai, Shuanghua (2016) Numerical methods for constrained Euclidean distance matrix optimization. University of Southampton, School of Mathematics, Doctoral Thesis, 169pp.

Record type: Thesis (Doctoral)

Abstract

This thesis is an accumulation of work regarding a class of constrained Euclidean Distance Matrix (EDM) based optimization models and corresponding numerical approaches. EDM-based optimization is powerful for processing distance information which appears in diverse applications arising from a wide range of fields, from which the motivation for this work comes. Those problems usually involve minimizing the error of distance measurements as well as satisfying some Euclidean distance constraints, which may present enormous challenge to the existing algorithms. In this thesis, we focus on problems with two different types of constraints. The first one consists of spherical constraints which comes from spherical data representation and the other one has a large number of bound constraints which comes from wireless sensor network localization.

For spherical data representation, we reformulate the problem as an Euclidean distance matrix optimization problem with a low rank constraint. We then propose an iterative algorithm that uses a quadratically convergent Newton-CG method at its each step. We study fundamental issues including constraint nondegeneracy and the nonsingularity of generalized Jacobian that ensure the quadratic convergence of the Newton method. We use some classic examples from the spherical multidimensional scaling to demonstrate the flexibility of the algorithm in incorporating various constraints.

For wireless sensor network localization, we set up a convex optimization model using EDM which integrates connectivity information as lower and upper bounds on the elements of EDM, resulting in an EDM-based localization scheme that possesses both efficiency and robustness in dealing with flip ambiguity under the presence of high level of noises in distance measurements and irregular topology of the concerning network of moderate size.

To localize a large-scale network efficiently, we propose a patching-stitching localization scheme which divides the network into several sub-networks, localizes each sub-network separately and stitching all the sub-networks together to get the recovered network. Mechanism for separating the network is discussed. EDM-based optimization model can be extended to add more constraints, resulting in a flexible localization scheme for various kinds of applications. Numerical results show that the proposed algorithm is promising.

Text
Shuanghua Bai final thesis.pdf - Other
Available under License University of Southampton Thesis Licence.
Download (13MB)

More information

Published date: July 2016
Organisations: University of Southampton, Mathematical Sciences

Identifiers

Local EPrints ID: 401542
URI: https://eprints.soton.ac.uk/id/eprint/401542
PURE UUID: f480a471-a56b-4d53-b71d-f508299d425e
ORCID for Hou-Duo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 27 Oct 2016 13:13
Last modified: 06 Oct 2018 00:35

Export record

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 https://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.

×