Ordinary Differential Equations and Applied Dynamics Commons^™

Sensitivity Analysis Of Basins Of Attraction For Nelder-Mead, Sonia K. Shah

Honors Projects

The Nelder-Mead optimization method is a numerical method used to find the minimum of an objective function in a multidimensional space. In this paper, we use this method to study functions - specifically functions with three-dimensional graphs - and create images of the basin of attraction of the function. Three different methods are used to create these images named the systematic point method, randomized centroid method, and systemized centroid method. This paper applies these methods to different functions. The first function has two minima with an equivalent function value. The second function has one global minimum and one local minimum. …