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dc.contributor.authorGilles, Marc Aurèle Tiberius
dc.date.accessioned2019-10-15T15:28:48Z
dc.date.available2019-10-15T15:28:48Z
dc.date.issued2019-05-30
dc.identifier.otherGilles_cornellgrad_0058F_11439
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:11439
dc.identifier.otherbibid: 11050245
dc.identifier.urihttps://hdl.handle.net/1813/67264
dc.description.abstractFour problems at the intersection of optimization and partial differential equations are presented. First, a problem in remote sensing of the marine atmospheric boundary layer is discussed. A method that exploits the low-rank structure of the electromagnetic field is used to infer the refractive index profile of the lower atmosphere. The second problem is concerned with 3D X-ray imaging of large objects at nanometer scale resolution. A massively parallel optimization method is used to perform the reconstruction from measurements of an object outside of the depth of focus. The third problem presents a path planning problem where an evader is choosing his trajectory to hinder the surveillance of an observer. An algorithm to compute optimal strategies using ideas from convex optimization, game theory and optimal control is described. The final chapter presents a practical framework to apply Krylov subspace methods to differential operators.
dc.language.isoen_US
dc.subjectApplied mathematics
dc.subjectOptimization
dc.subjectDifferential equations
dc.subjectKrylov subspaces
dc.subjectPath planning
dc.subjectInverse Problems
dc.titleAt the intersection of differential equations and optimization: inverse problems, path planning and Krylov subspaces
dc.typedissertation or thesis
thesis.degree.disciplineApplied Mathematics
thesis.degree.grantorCornell University
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh.D., Applied Mathematics
dc.contributor.chairTownsend, Alex John
dc.contributor.committeeMemberVladimirsky, Alexander B.
dc.contributor.committeeMemberEarls, Christopher J.
dc.contributor.committeeMemberBindel, David S.
dcterms.licensehttps://hdl.handle.net/1813/59810
dc.identifier.doihttps://doi.org/10.7298/gjf7-7q66


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