| 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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| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
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| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
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etd.pdf |
794.17 Kb |
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