The determination of structured Hessian matrices via automatic differentiation

dc.contributor.authorEmbaye, Samuel
dc.date.accessioned2014-09-23T17:17:37Z
dc.date.available2014-09-23T17:17:37Z
dc.date.issued2014-09-23
dc.date.submitted2014
dc.description.abstractIn using automatic differentiation (AD) for Hessian computation, efficiency can be achieved by exploiting the sparsity existing in the derivative matrix. However, in the case where the Hessian is dense, this cannot be done and the space requirements to compute the Hessian can become very large. But if the underlying function can be expressed in a structured form, a “deeper” sparsity can be exploited to minimize the space requirement. In this thesis, we provide a summary of automatic differentiation (AD) techniques, as applied to Jacobian and Hessian matrix determination, as well as the graph coloring techniques involved in exploiting their sparsity. We then discuss how structure in the underlying function can be used to greatly improve efficiency in gradient/Jacobian computation. We then propose structured methods for Hessian computation that substantially reduce the space required. Finally, we propose a method for Hessian computation where the structure of the function is not provided.en
dc.identifier.urihttp://hdl.handle.net/10012/8850
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectautomatic differentiationen
dc.subjectstructureen
dc.subjectgradienten
dc.subjectHessianen
dc.subject.programCombinatorics and Optimizationen
dc.titleThe determination of structured Hessian matrices via automatic differentiationen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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