Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming

Authors:
Abdo Y. Alfakih;Amir Khandani;Henry Wolkowicz
Affiliations:
University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario N2L 3G1, Canada. aalfakih@orion.math.uwaterloo.ca;University of Waterloo, Department of Electrical & Computer Engineering, Waterloo, Ontario N2L 3G1, Canada. khandani@claude.uwaterloo.ca;University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario N2L 3G1, Canada. henry@orion.math.uwaterloo.ca
Venue:
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Year:
1999

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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 elementsof 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 thecompletion 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 androbustness of our approach. Our randomly generated problemsconsistently resulted in low dimensional solutions when no completionexisted.