Date Thesis Awarded

2000

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Computer Science

Advisor

Virginia Torczon

Committee Member

Weizhen Mao

Committee Member

Michael W. Trosset

Abstract

It is often a desire in many fields such as mathematics, physics, and engineering to solve bound constrained minimization problems. Non-derivative based direct search methods each use a specific method of function sampling in an attempt to home in on the minimizers of a given function. Here we focus on threes simplex based direct search methods: the original simplex search provided by the description of Spendley,Hext and Himsworth; a variation on its theme provided by Nelder and Mead; and a sequential version of Torczon's multidirectional search. It is a common assumption that these searches are easily implemented and used. This research addresses this claim and suggests that these searches are more intricate and should be implemented and used in a careful fashion.We first provide a formal description of each algorithm using a common notation, providing a means of direct comparison between algorithms. We then discuss the importance of resolving seemingly small ambiguities in these algorithms before using them for optimization. For this, we provide an anomaly specific to the Nelder-Mead algorithm in which the search fails to converge to a constrained stationary point. We conclude with some preliminary results of execution of these algorithms on a specific set of objective functions.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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