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Simplex Search Behavior in Nonlinear Optimization
Gurson, Adam P.
Gurson, Adam P.
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.
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Migrated from Dspace in 2016.
Date
2000-01-01
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Keywords
Mathematical optimization, Nonlinear programming, Algorithms
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Department
Computer Science