Comparing SOS and SDP relaxations of sensor network localization
- 224 Downloads
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.
KeywordsSensor network localization Semidefinite programming relaxation Sum of squares relaxation Individual trace
Unable to display preview. Download preview PDF.
- 3.Biswas, P., Ye, Y.: Semidefinite programming for ad hoc wireless sensor network localization. In: Proc. 3rd IPSN, Berkeley, CA, pp. 46–54 (2004) Google Scholar
- 7.Doherty, L., Pister, K.S.J., El Ghaoui, L.: Convex position estimation in wireless sensor networks. In: Proc. 20th INFOCOM, Los Alamitos, CA, vol. 3, pp. 1655–1663 (2001) Google Scholar
- 9.Krislock, N., Piccialli, V., Wolkowicz, H.: Robust semidefinite programming approaches for sensor network localization with anchors. Report, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, May 2006 Google Scholar
- 10.Krislock, N., Rendl, F., Wolkowiz, H.: Noisy sensor network localization using semidefinite representations and facial reduction. Report, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, March 2010 Google Scholar
- 12.Krislock, N., Wolkowicz, H.: Euclidean distance matrices and applications. In: Handbook of Semidefinite, Cone and Polynomial Optimization: Theory, Algorithms, Software and Applications Google Scholar
- 17.Sturm, J.F.: Using Se.Du.Mi. 1.02, A Matlab∗ toolbox for optimization over symmetric cones (updated for Version 1.05). Report, Department of Econometrics, Tilburg University, Tilburg, August 1998–October 2001 Google Scholar