/lp/springer-journals/solving-euclidean-distance-matrix-completion-problems-via-semidefinite-vru2009bMm
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- Publisher
- Springer Journals
- Copyright
- Copyright © 1999 by Kluwer Academic Publishers
- Subject
- Mathematics; Optimization; Operations Research, Management Science; Operation Research/Decision Theory; Statistics, general; Convex and Discrete Geometry
- ISSN
- 0926-6003
- eISSN
- 1573-2894
- DOI
- 10.1023/A:1008655427845
- Publisher site
- See Article on Publisher Site
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.
Journal
Computational Optimization and Applications – Springer Journals
Published: Oct 20, 2004