A New Algorithm for Global Minimization Based on the Combination of Adaptive Random Search and Simplex Algorithm of Nelder and Mead

We propose a new general-purpose algorithm for locating global minima of differentiable and nondifferentiable multivariable functions. The algorithm is based on combination of the adaptive random search approach and the Nelder-Mead simplex minimization. We show that the new hybrid algorithm satisfies the conditions of the theorem for convergence (in probability) to global minimum. By using test functions we demonstrate that the proposed algorithm is far more efficient than the pure adaptive random search algorithm. Some of the considered test functions are related to membership set estimation method for model parameter determination which was successfully applied to kinetic problems in chemistry and biology.