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Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming

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Abstract

Given a partial symmetric matrix A with only certain elements specified, the Euclidean distance matrix completion problem (EDMCP) is to find the unspecified elements of A that make A a Euclidean distance matrix (EDM). In this paper, we follow the successful approach in [20] and solve the EDMCP by generalizing the completion problem to allow for approximate completions. In particular, we introduce a primal-dual interior-point algorithm that solves an equivalent (quadratic objective function) semidefinite programming problem (SDP). Numerical results are included which illustrate the efficiency and robustness of our approach. Our randomly generated problems consistently resulted in low dimensional solutions when no completion existed.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Abdo Y. Alfakih

  2. Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Amir Khandani

  3. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Henry Wolkowicz

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  1. Abdo Y. Alfakih
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  2. Amir Khandani
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  3. Henry Wolkowicz
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Alfakih, A.Y., Khandani, A. & Wolkowicz, H. Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming. Computational Optimization and Applications 12, 13–30 (1999). https://doi.org/10.1023/A:1008655427845

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