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Recently, a semidefinite programming (SDP) relaxation approach has been proposed to solve the sensor network localization problem. Although it achieves high accuracy in estimating the sensor locations, the speed of the SDP approach is not satisfactory for practical applications. In this paper we propose methods to further relax the SDP relaxation, more precisely, to relax the single semidefinit...

Many signal processing applications reduce to solving integer least square problems, e.g., Maximum Likelihood (ML) detection, which is NP-hard. Recently semidefinite programming (SDP) approach has been shown to be promising approach to combinatorial problems. SDP methods have been applied to the communications problem, e.g., [1], [2], [3]. But so far no theoretical analysis of the algorithm is ...

We present a survey on the sparse SDP relaxation proposed as a sparse variant of Lasserre’s SDP relaxation of polynomial optimization problems. We discuss the primal and dual approaches to derive the sparse SDP and SOS relaxations, and their relationship. In particular, exploiting structured sparsity in the both approaches is described in view of the quality and the size of the SDP relaxations....

BACKGROUND Maternal smoking during pregnancy (SDP) has been studied extensively as a risk factor for adverse offspring outcomes and is known to co-occur with other familial risk factors. Accounting for general familial risk factors has attenuated associations between SDP and adverse offspring outcomes, and identifying these confounds will be crucial to elucidating the relationship between SDP a...

The sensor network localization, SNL , problem in embedding dimension r, consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the sensors (called anchors). Current solution techniques relax this problem to a weighted, nearest, (positive) semidefinite programming, SDP , completion problem, by...