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
143-170
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
23 June 2014
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), .
(doi:10.1007/s40305-014-0048-9).
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.
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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: http://eprints.soton.ac.uk/id/eprint/367409
ISSN: 2194-668X
PURE UUID: 872612ac-581a-4718-925e-fdfe371661d4
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Date deposited: 29 Jul 2014 13:54
Last modified: 15 Mar 2024 03:21
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