Modifications of the Nelder-Mead simplex method for stochastic simulation response optimization

It is pointed out that the Nelder-Mead simplex method rescaling and shrinking steps make it sensitive to random variations in the response function values, and introduce risks of false convergence on stochastic functions. The authors give analytical and empirical evidence that characterizes false convergence on stochastic functions, and discuss several modifications to reduce the likelihood of false convergence. They describe a computational comparison of several modifications when used to optimize simple stochastic functions of two and ten variables.<>