Handbook on Semidefinite, Conic and Polynomial Optimization

Volume 166 of the series International Series in Operations Research & Management Science pp 879-914


Euclidean Distance Matrices and Applications

  • Nathan KrislockAffiliated withDepartment of Combinatorics and Optimization, University of Waterloo Email author 
  • , Henry WolkowiczAffiliated withDepartment of Combinatorics and Optimization, University of Waterloo

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Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especially the problem of wireless sensor network localization, have all become very active areas of research. The second reason for this increased interest is the close connection between EDMs and semidefinite matrices. Our recent ability to solve semidefinite programs efficiently means we can now also solve many problems involving EDMs efficiently. This chapter connects the classical approaches for EDMs with the more recent tools from semidefinite programming. We emphasize the application to sensor network localization.