The University of Southampton
University of Southampton Institutional Repository

Conditional quadratic semidefinite programming: examples and methods

Conditional quadratic semidefinite programming: examples and methods
Conditional quadratic semidefinite programming: examples and methods
The conditional quadratic semidefinite programming (cQSDP) refers to a class of matrix optimization problems whose matrix variables are required to be positive semidefinite on a subspace, and the objectives are quadratic. The chief purpose of this paper is to focus on two primal examples of cQSDP: the problem of matrix completion/approximation on a subspace and the Euclidean distance matrix problem. For the latter problem, we review some classical contributions and establish certain links among them. Moreover, we develop a semismooth Newton method for a special class of cQSDP and establish its quadratic convergence under the condition of constraint nondegeneracy. We also include an application in calibrating the correlation matrix in Libor market models. We hope this work will stimulate new research in cQSDP.
matrix optimization, conditional semidefinite programming, euclidean distance matrix, semismooth newton method, 49M45, 90C25, 90C33
2194-668X
143-170
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85

Qi, Hou-Duo (2014) Conditional quadratic semidefinite programming: examples and methods. Journal of the Operations Research Society of China, 2 (2), 143-170. (doi:10.1007/s40305-014-0048-9).

Record type: Article

Abstract

The conditional quadratic semidefinite programming (cQSDP) refers to a class of matrix optimization problems whose matrix variables are required to be positive semidefinite on a subspace, and the objectives are quadratic. The chief purpose of this paper is to focus on two primal examples of cQSDP: the problem of matrix completion/approximation on a subspace and the Euclidean distance matrix problem. For the latter problem, we review some classical contributions and establish certain links among them. Moreover, we develop a semismooth Newton method for a special class of cQSDP and establish its quadratic convergence under the condition of constraint nondegeneracy. We also include an application in calibrating the correlation matrix in Libor market models. We hope this work will stimulate new research in cQSDP.

Text
submission_version_R1.pdf - Author's Original
Download (761kB)

More information

Published date: 23 June 2014
Keywords: matrix optimization, conditional semidefinite programming, euclidean distance matrix, semismooth newton method, 49M45, 90C25, 90C33
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 367409
URI: https://eprints.soton.ac.uk/id/eprint/367409
ISSN: 2194-668X
PURE UUID: 872612ac-581a-4718-925e-fdfe371661d4
ORCID for Hou-Duo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 29 Jul 2014 13:54
Last modified: 03 Dec 2019 01:48

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 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.

×