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SIAM J. on Optimization / Volume 20 / Issue 1

SIAM J. Optim. 20, pp. 192-215 (24 pages)

Exploiting Sparsity in SDP Relaxation for Sensor Network Localization

Sunyoung Kim, Masakazu Kojima, and Hayato Waki

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A sensor network localization problem can be formulated as a quadratic optimization problem (QOP). For QOPs, semidefinite programming (SDP) relaxation by Lasserre with relaxation order 1 for general polynomial optimization problems (POPs) is known to be equivalent to the sparse SDP relaxation by Waki et al. with relaxation order 1, except for the size and sparsity of the resulting SDP relaxation problems. We show that the sparse SDP relaxation applied to the QOP is at least as strong as the Biswas–Ye SDP relaxation for the sensor network localization problem. A sparse variant of the Biswas–Ye SDP relaxation, which is equivalent to the original Biswas–Ye SDP relaxation, is also derived. We compare numerically the sparse SDP relaxation applied to the QOP, the Biswas–Ye SDP relaxation, its sparse variant, and the edge-based SDP relaxation by Wang et al. to confirm the effectiveness of the proposed techniques for exploiting the sparsity in SDP relaxation for sensor network localization problems. The sparse SDP relaxation applied to the QOP is much faster than the Biswas–Ye SDP relaxation, and the sparse variant of the Biswas–Ye SDP relaxation outperforms all other SDP relaxations in speed.

© 2009 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

65K05, 90C22, 90C35

PUBLICATION DATA

ISSN

1052-6234 (print)  
1095-7189 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received January 15, 2008
Accepted October 13, 2008
Published online April 01, 2009
Digital Object Identifier
http://dx.doi.org/10.1137/080713380

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