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Noisy Euclidean distance matrix completion with a single missing node

Author

Listed:
  • Stefan Sremac

    (University of Waterloo)

  • Fei Wang

    (Royal Institute of Technology)

  • Henry Wolkowicz

    (University of Waterloo)

  • Lucas Pettersson

    (Royal Institute of Technology)

Abstract

We present several solution techniques for the noisy single source localization problem, i.e. the Euclidean distance matrix completion problem with a single missing node to locate under noisy data. For the case that the sensor locations are fixed, we show that this problem is implicitly convex, and we provide a purification algorithm along with the SDP relaxation to solve it efficiently and accurately. For the case that the sensor locations are relaxed, we study a model based on facial reduction. We present several approaches to solve this problem efficiently, and we compare their performance with existing techniques in the literature. Our tools are semidefinite programming, Euclidean distance matrices, facial reduction, and the generalized trust region subproblem. We include extensive numerical tests.

Suggested Citation

  • Stefan Sremac & Fei Wang & Henry Wolkowicz & Lucas Pettersson, 2019. "Noisy Euclidean distance matrix completion with a single missing node," Journal of Global Optimization, Springer, vol. 75(4), pages 973-1002, December.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:4:d:10.1007_s10898-019-00825-7
    DOI: 10.1007/s10898-019-00825-7
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    References listed on IDEAS

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    1. Ting Pong & Henry Wolkowicz, 2014. "The generalized trust region subproblem," Computational Optimization and Applications, Springer, vol. 58(2), pages 273-322, June.
    2. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    3. Gábor Pataki, 1998. "On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 339-358, May.
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