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Comparing SOS and SDP relaxations of sensor network localization


  • João Gouveia


  • Ting Pong



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. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • João Gouveia & Ting Pong, 2012. "Comparing SOS and SDP relaxations of sensor network localization," Computational Optimization and Applications, Springer, vol. 52(3), pages 609-627, July.
  • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:609-627
    DOI: 10.1007/s10589-011-9431-1

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    References listed on IDEAS

    1. Jiawang Nie, 2009. "Sum of squares method for sensor network localization," Computational Optimization and Applications, Springer, vol. 43(2), pages 151-179, June.
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    Cited by:

    1. Chao Ding & Hou-Duo Qi, 2017. "Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation," Computational Optimization and Applications, Springer, vol. 66(1), pages 187-218, January.


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