Universal rigidity: towards accurate and efficient localization of wireless networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
Exploiting structured sparsity in large scale semidefinite programming problems
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Explicit Sensor Network Localization using Semidefinite Representations and Facial Reductions
SIAM Journal on Optimization
Universal Rigidity and Edge Sparsification for Sensor Network Localization
SIAM Journal on Optimization
ACM Transactions on Mathematical Software (TOMS)
Computational Optimization and Applications
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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.