The Clarke Derivative and Set-Valued Mappings in the Numerical Optimization of Non-Smooth, Noisy Functions

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dc.contributor.authorKrahnke, Andreasen
dc.contributor.committeechairSachs, Ekkehard W.en
dc.contributor.committeememberDay, Martin V.en
dc.contributor.committeememberRogers, Robert C.en
dc.contributor.committeememberKing, Belinda B.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:34:50Zen
dc.date.adate2001-05-04en
dc.date.available2014-03-14T20:34:50Zen
dc.date.issued2001-04-30en
dc.date.rdate2002-05-04en
dc.date.sdate2001-05-03en
dc.description.abstractIn this work we present a new tool for the convergence analysis of numerical optimization methods. It is based on the concepts of the Clarke derivative and set-valued mappings. Our goal is to apply this tool to minimization problems with non-smooth and noisy objective functions. After deriving a necessary condition for minimizers of such functions, we examine two unconstrained optimization routines. First, we prove new convergence theorems for Implicit Filtering and General Pattern Search. Then we show how these results can be used in practice, by executing some numerical computations.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-05032001-183707en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05032001-183707/en
dc.identifier.urihttp://hdl.handle.net/10919/32132en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartetd.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectImplicit Filteringen
dc.subjectNoisy Objective Functionen
dc.subjectPattern Searchen
dc.subjectNon-smooth Optimizationen
dc.subjectSet-Valued Mappingen
dc.subjectClarke Derivativeen
dc.titleThe Clarke Derivative and Set-Valued Mappings in the Numerical Optimization of Non-Smooth, Noisy Functionsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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