Abstract
In this paper, we strengthen the edge-based semidefinite programming relaxation (ESDP) recently proposed by Wang, Zheng, Boyd, and Ye (SIAM J. Optim. 19:655-673, 2008) by adding lower bound constraints. We show that, when distances are exact, zero individual trace is necessary and sufficient for a sensor to be correctly positioned by an interior solution. To extend this characterization of accurately positioned sensors to the noisy case, we propose a noise-aware version of ESDPlb(ρ-ESDPlb) and show that, for small noise, a small individual trace is equivalent to the sensor being accurately positioned by a certain analytic center solution. We then propose a postprocessing heuristic based on ρ-ESDPlband a distributed algorithm to solve it. Our computational results show that, when applied to a solution obtained by solving ρ-ESDP proposed of Pong and Tseng (Math. Program. doi: 10.1007/s10107-009-0338-x ), this heuristics usually improves the RMSD by at least 10%. Furthermore, it provides a certificate for identifying accurately positioned sensors in the refined solution, which is not common for existing refinement heuristics.
Original language | English |
---|---|
Pages (from-to) | 23-44 |
Number of pages | 22 |
Journal | Computational Optimization and Applications |
Volume | 53 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Sept 2012 |
Externally published | Yes |
Keywords
- Coordinate gradient descent
- Error bound
- Log-barrier
- Semidefinite programming relaxation
- Sensor network localization
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Applied Mathematics