Nelder-Mead method is one of the most used methods for minimization of multivariable functions. In this thesis we present the problem of minimization of nonlinear multivariable functions and several methods which are used to solve this problem. We describe the gradient descent method, conjugate gradient method, Powell's method, Spendley-Hext-Himsworth method and Nelder-Mead method. We analyze how the latter works and we test its success at minimizing different functions. We point out problems that appear during the execution of the algorithm and analyze possible improvements.
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