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Comparing SOS and SDP relaxations of sensor network localization

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Abstract

We investigate the relationships between various sum of squares (SOS) and semidefinite programming (SDP) relaxations for the sensor network localization problem. In particular, we show that Biswas and Ye’s SDP relaxation is equivalent to the degree one SOS relaxation of Kim et al. We also show that Nie’s sparse-SOS relaxation is stronger than the edge-based semidefinite programming (ESDP) relaxation, and that the trace test for accuracy, which is very useful for SDP and ESDP relaxations, can be extended to the sparse-SOS relaxation.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195, USA

    João Gouveia & Ting Kei Pong

  2. CMUC, Department of Mathematics, University of Coimbra, 3001-454, Coimbra, Portugal

    João Gouveia

Authors
  1. João Gouveia
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  2. Ting Kei Pong
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Correspondence to João Gouveia.

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Gouveia, J., Pong, T.K. Comparing SOS and SDP relaxations of sensor network localization. Comput Optim Appl 52, 609–627 (2012). https://doi.org/10.1007/s10589-011-9431-1

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  • DOI: https://doi.org/10.1007/s10589-011-9431-1

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