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Comparing SOS and SDP relaxations of sensor network localization

Joćo Gouveia (jgouveia***at***math.washington.edu)
Ting Kei Pong (tkpong***at***math.washington.edu)

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.

Keywords: Sensor network localization, semidefinite programming relaxation, sum of squares relaxation, individual trace.

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Submitted to Computational Optimization and its Applications

Download: [PDF]

Entry Submitted: 10/08/2010
Entry Accepted: 10/08/2010
Entry Last Modified: 03/27/2011

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