High-dimensional integration for optimization under uncertainty

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dc.contributor.advisorHeinkenschloss, Matthias
dc.contributor.committeeMemberSorensen, Danny C
dc.contributor.committeeMemberZhang, Yin
dc.creatorTakhtaganov, Timur A
dc.date.accessioned2016-01-07T20:42:44Z
dc.date.available2016-01-07T20:42:44Z
dc.date.created2015-12
dc.date.issued2015-09-09
dc.date.submittedDecember 2015
dc.date.updated2016-01-07T20:42:44Z
dc.description.abstractThis thesis focuses on the problem of evaluating high-dimensional integrals arising in optimization under uncertainty. Uncertainties in the input data affect the behavior of the physical system and need to be accounted for at the design stage or in the way the system is controlled. This translates into evaluating integrals of the quantities of interest with respect to the random parameters. This task becomes challenging when the dimension of the random parameters is high. Without guidelines for the choice of favorable integration methods the optimization algorithm might encounter prohibitively high computational cost. This thesis provides a comprehensive overview of methods for high-dimensional integration and exposes their relative strengths and weaknesses. Emphasis is placed on problems with moderately high dimension and with non-smoothness. The performance of integration methods in high dimension is assessed on several simple model problems.
dc.format.mimetypeapplication/pdf
dc.identifier.citationTakhtaganov, Timur A. "High-dimensional integration for optimization under uncertainty." (2015) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/87771">https://hdl.handle.net/1911/87771</a>.
dc.identifier.urihttps://hdl.handle.net/1911/87771
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectoptimization under uncertainty
dc.subjecthigh-dimensional integration
dc.subjectrisk measures
dc.subjectsparse grids
dc.subjectuncertainty quantification
dc.titleHigh-dimensional integration for optimization under uncertainty
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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