Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization
SIAM Journal on Optimization
Global Continuation for Distance Geometry Problems
SIAM Journal on Optimization
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Semidefinite programming for ad hoc wireless sensor network localization
Proceedings of the 3rd international symposium on Information processing in sensor networks
Sparsity in sums of squares of polynomials
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Minimizing Polynomials via Sum of Squares over the Gradient Ideal
Mathematical Programming: Series A and B
Theory of semidefinite programming for Sensor Network Localization
Mathematical Programming: Series A and B
Second-Order Cone Programming Relaxation of Sensor Network Localization
SIAM Journal on Optimization
ACM Transactions on Mathematical Software (TOMS)
Computing sum of squares decompositions with rational coefficients
Theoretical Computer Science
Wireless sensor networks localization with isomap
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Universal Rigidity and Edge Sparsification for Sensor Network Localization
SIAM Journal on Optimization
ACM Transactions on Mathematical Software (TOMS)
Computational Optimization and Applications
Hi-index | 0.00 |
We formulate the sensor network localization problem as finding the global minimizer of a quartic polynomial. Then sum of squares (SOS) relaxations can be applied to solve it. However, the general SOS relaxations are too expensive to implement for large problems. Exploiting the special features of this polynomial, we propose a new structured SOS relaxation, and discuss its various properties. When distances are given exactly, this SOS relaxation often returns true sensor locations. At each step of interior point methods solving this SOS relaxation, the complexity is $\mathcal{O}(n^{3})$ , where n is the number of sensors. When the distances have small perturbations, we show that the sensor locations given by this SOS relaxation are accurate within a constant factor of the perturbation error under some technical assumptions. The performance of this SOS relaxation is tested on some randomly generated problems.