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Semidefinite Programming Relaxations of the Simplified Wasserstein Barycenter Problem: An ADMM Approach

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dc.contributor.authorCheng, Jiahui
dc.date.accessioned2023-05-04T16:01:50Z
dc.date.available2023-05-04T16:01:50Z
dc.date.issued2023-05-04
dc.date.submitted2023-04-28
dc.description.abstractThe Simplified Wasserstein Barycenter problem, the problem of picking k points each chosen from a distinct set of n points as to minimize the sum of distances to their barycenter, finds applications in various areas of data science. Despite the simple formulation, it is a hard computational problem. The difficulty comes in the lack of efficient algorithms for approximating the solution. In this thesis, I propose a doubly non-negative relaxation to this problem and apply the alternating direction method of multipliers (ADMM) with intermediate update of multipliers, to efficiently compute tight lower and upper bounds on its optimal value for certain input data distributions. Our empirics show that generically the gap between upper and lower bounds is zero, though problems with symmetries exhibit positive gaps.en
dc.identifier.urihttp://hdl.handle.net/10012/19416
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectcontinuous optimizationen
dc.subjectsemidefinite programming relaxationen
dc.subjectWasserstein Barycentersen
dc.subjectalternating direction method of multipliersen
dc.subjectdoubly non-negative relaxationen
dc.subjectPeaceman-Rachford splitting methoden
dc.subjectprojection methoden
dc.subjectsplitting methoden
dc.subjectconvex relaxationen
dc.subjectsimplified Wasserstein Barycentersen
dc.titleSemidefinite Programming Relaxations of the Simplified Wasserstein Barycenter Problem: An ADMM Approachen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimizationen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.embargo.terms0en
uws.contributor.advisorWolkowicz, Henry
uws.contributor.advisorMoursi, Walaa
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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