Type of Document Master's Thesis Author Krahnke, Andreas Author's Email Address email@example.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 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.
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