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Nonsmooth Newton Methods for Solving the Best Approximation Problem; with Applications to Linear Programming

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dc.contributor.authorWeames, Tyler
dc.date.accessioned2023-12-19T14:12:04Z
dc.date.available2023-12-19T14:12:04Z
dc.date.issued2023-12-19
dc.date.submitted2023-12-18
dc.description.abstractIn this thesis, we study the effects of applying a modified Levenberg-Marquardt regularization to a nonsmooth Newton method. We expand this application to exact and inexact nonsmooth Newton methods and apply it to the best approximation constrained to a polyhedral set problem. We also demonstrate that linear programs can be represented as a best approximation problem, extending the application of nonsmooth Newton methods to linear programming. This application provides us with insight into an external path following algorithm that, like the simplex method, takes a finite number of steps on the boundary of the polyhedral set. However, unlike the simplex method, these steps do not use basic feasible solutions.en
dc.identifier.urihttp://hdl.handle.net/10012/20179
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.relation.urihttps://www.math.uwaterloo.ca/~hwolkowi/henry/reports/projpolyhLPwR.d/en
dc.subjectnonsmooth Newton methoden
dc.subjectGauss-Newton methoden
dc.subjectLevenberg-Marquardt regularizationen
dc.subjectexact and inexact methodsen
dc.subjectbest approximation problemen
dc.subjectfirst order methodsen
dc.subjectsecond order methodsen
dc.subjectlinear programmingen
dc.subjectsensitivity analysisen
dc.subjecttime complexityen
dc.titleNonsmooth Newton Methods for Solving the Best Approximation Problem; with Applications to Linear Programmingen
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.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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Combinatorics and Optimization