Semidefinite Facial Reduction for Low-Rank Euclidean Distance Matrix Completion

dc.contributor.authorKrislock, Nathan
dc.date.accessioned2010-04-27T21:04:44Z
dc.date.available2010-04-27T21:04:44Z
dc.date.issued2010-04-27T21:04:44Z
dc.date.submitted2010
dc.description.abstractThe main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.en
dc.identifier.urihttp://hdl.handle.net/10012/5093
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.subjectEuclidean distance matricesen
dc.subjectlow-rank matrix completionen
dc.subjectsemidefinite relaxationsen
dc.subjectfacial reductionen
dc.subjectwireless sensor network localizationen
dc.subjectmolecular conformationen
dc.subject.programCombinatorics and Optimizationen
dc.titleSemidefinite Facial Reduction for Low-Rank Euclidean Distance Matrix Completionen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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