A facial reduction approach for the single source localization problem

He Shi and Qingna Li ()
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He Shi: Beijing Institute of Technology
Qingna Li: Beijing Institute of Technology/Key Laboratory of Mathematical Theory and Computation in Information Security

Journal of Global Optimization, 2023, vol. 87, issue 2, No 22, 855 pages

Abstract: Abstract The single source localization problem (SSLP) appears in several fields such as signal processing and global positioning systems. The optimization problem of SSLP is nonconvex and difficult to find its globally optimal solution. It can be reformulated as a rank constrained Euclidean distance matrix (EDM) completion problem with a number of equality constraints. In this paper, we propose a facial reduction approach to solve such an EDM completion problem. For the constraints of fixed distances between sensors, we reduce them to a face of the EDM cone and derive the closed formulation of the face. We prove constraint nondegeneracy for each feasible point of the resulting EDM optimization problem without a rank constraint, which guarantees the quadratic convergence of semismooth Newton’s method. To tackle the nonconvex rank constraint, we apply the majorized penalty approach developed by Zhou et al. (IEEE Trans Signal Process 66(3):4331-4346, 2018). Numerical results verify the fast speed of the proposed approach while giving comparable quality of solutions as other methods.

Keywords: Single source localization; Euclidean distance matrix; Facial reduction; Majorized penalty approach; Constraint nondegeneracy (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01188-2

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