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dc.contributor.authorKrahnke, Andreasen_US
dc.date.accessioned2014-03-14T20:34:50Z
dc.date.available2014-03-14T20:34:50Z
dc.date.issued2001-04-30en_US
dc.identifier.otheretd-05032001-183707en_US
dc.identifier.urihttp://hdl.handle.net/10919/32132
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_US
dc.publisherVirginia Techen_US
dc.relation.haspartetd.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectImplicit Filteringen_US
dc.subjectNoisy Objective Functionen_US
dc.subjectPattern Searchen_US
dc.subjectNon-smooth Optimizationen_US
dc.subjectSet-Valued Mappingen_US
dc.subjectClarke Derivativeen_US
dc.titleThe Clarke Derivative and Set-Valued Mappings in the Numerical Optimization of Non-Smooth, Noisy Functionsen_US
dc.typeThesisen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreeMaster of Scienceen_US
thesis.degree.nameMaster of Scienceen_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairSachs, Ekkehard W.en_US
dc.contributor.committeememberDay, Martin V.en_US
dc.contributor.committeememberRogers, Robert C.en_US
dc.contributor.committeememberKing, Belinda B.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05032001-183707/en_US
dc.date.sdate2001-05-03en_US
dc.date.rdate2002-05-04
dc.date.adate2001-05-04en_US


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