caa a22 4500 475750446 CHVBK 20180406123522.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1023/A:1008722907820 doi (NATIONALLICENCE)springer-10.1023/A:1008722907820 Trosset Michael Department of Mathematics, College of William & Mary, P.O. Box 8795, 23187-8795, Williamsburg, VA, USA aut Distance Matrix Completion by Numerical Optimization [Elektronische Daten] [Michael Trosset] Consider the problem of determining whether or not a partial dissimilarity matrix can be completed to a Euclidean distance matrix. The dimension of the distance matrix may be restricted and the known dissimilarities may be permitted to vary subject to bound constraints. This problem can be formulated as an optimization problem for which the global minimum is zero if and only if completion is possible. The optimization problem is derived in a very natural way from an embedding theorem in classical distance geometry and from the classical approach to multidimensional scaling. It belongs to a general family of problems studied by Trosset (Technical Report 97-3, Department of Computational & Applied Mathematics—MS 134, Rice University, Houston, TX 77005-1892, 1997) and can be formulated as a nonlinear programming problem with simple bound constraints. Thus, this approach provides a constructive technique for obtaining approximate solutions to a general class of distance matrix completion problems. Kluwer Academic Publishers, 2000 Euclidean distance matrices nationallicence positive semidefinite matrices nationallicence distance geometry nationallicence multidimensional scaling nationallicence Computational Optimization and Applications Kluwer Academic Publishers 17/1(2000-10-01), 11-22 0926-6003 17:1<11 2000 17 10589 https://doi.org/10.1023/A:1008722907820 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008722907820 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Trosset Michael Department of Mathematics, College of William & Mary, P.O. Box 8795, 23187-8795, Williamsburg, VA, USA aut NATIONALLICENCE 773 0- Computational Optimization and Applications Kluwer Academic Publishers 17/1(2000-10-01), 11-22 0926-6003 17:1<11 2000 17 10589 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer