Title page for ETD etd-05032001-183707


Type of Document Master's Thesis
Author Krahnke, Andreas
Author's Email Address akrahnke@hotmail.com
URN etd-05032001-183707
Title The Clarke Derivative and Set-Valued Mappings in the Numerical Optimization of Non-Smooth, Noisy Functions
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Sachs, Ekkehard W. Committee Chair
Day, Martin V. Committee Member
King, Belinda B. Committee Member
Rogers, Robert C. Committee Member
Keywords
  • Implicit Filtering
  • Noisy Objective Function
  • Pattern Search
  • Non-smooth Optimization
  • Set-Valued Mapping
  • Clarke Derivative
Date of Defense 2001-04-30
Availability unrestricted
Abstract
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.

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