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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2001

Author dc:creator

• Krahnke, Andreas

Chair dc:contributor.committeechair

• Sachs, Ekkehard W.

Committee members dc:contributor.committeemember

• Day, Martin V.
• Rogers, Robert C.
• King, Belinda B.

• Implicit Filtering
• Noisy Objective Function
• Pattern Search
• Non-smooth Optimization
• Set-Valued Mapping
• Clarke Derivative

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-05032001-183707

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32132