Dissertation
DIRECTIONAL DIRECT-SEARCH OPTIMIZATION METHODS WITH POLLING DIRECTIONS BASED ON EQUAL ANGLE DISTRIBUTIONS
Doctor of Philosophy (PhD), Washington State University
01/2012
Handle:
https://hdl.handle.net/2376/4697
Abstract
Strategies for directional direct-search methods are introduced, including new instances of the Mesh Adaptive Direct Search (Mads) and the Generating Set Search (Gss) class of algorithms, which utilize a more uniform distribution of search directions when compared to other strategies. These strategies base their poll directions on positive bases having an equal angle distribution through the use of the QR decomposition to obtain an orthogonal set of directions or on generat- ing a regular simplex centered at the origin with vertices on the unit sphere. The distribution of directions is the key to enhanced performance in high dimensions and for constrained problems. Analysis is presented to show that the use of the QR decomposition or regular simplices within the Mads framework is valid and that all the convergence results from the optimization literature are maintained. Finally, a variety of tests are presented on smooth, nonsmooth, unconstrained and constrained problems. The results between various instances of directional direct-search methods on identical sets of test problems are compared.
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Details
- Title
- DIRECTIONAL DIRECT-SEARCH OPTIMIZATION METHODS WITH POLLING DIRECTIONS BASED ON EQUAL ANGLE DISTRIBUTIONS
- Creators
- Benjamin Van Dyke
- Contributors
- Thomas J Asaki (Advisor)Kevin R Vixie (Committee Member)Bala Krishnamoorthy (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 129
- Identifiers
- 99900581653001842
- Language
- English
- Resource Type
- Dissertation