Hybrid initialization for non-convex network localization problems

Abstract

Solving the distance-based network localization problem typically entails the formulation of an equivalent optimization problem which is either convex but sub-optimal, or optimal (i.e., maximum-likelihood) but non-convex. We show that the non-convexity implied by the choice of an optimal formulation need not be translated onto high computational complexity nor to performance degradation. To this end, we focus on an approach whereby low-complexity optimization algorithms are coupled with an efficient initialization which in turn, is formulated in terms of an Euclidean Distance Matrix (EDM) completion problem under the condition that the network is percolated (as required by Graph-based Completion). The resulting Hybrid Initialization scheme is shown to be sufficient to bring the performance of low-complexity algorithms such as the SMACOF and the NLS close to that of far more sophisticated alternatives such as the SDP.