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

In 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. / Master of Science

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/32132
Date04 May 2001
CreatorsKrahnke, Andreas
ContributorsMathematics, Sachs, Ekkehard W., Day, Martin V., Rogers, Robert C., King, Belinda B.
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
LanguageEnglish
Detected LanguageEnglish
TypeThesis
Formatapplication/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/
Relationetd.pdf

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