An unconstrained minimization technique using successive implementations of Golden Search algorithm

Abstract

In this paper, we propose a new technique in solving the minimum of a function defined on a ball centered at x0 with radius ρ¯ using successive implementations of Golden Search algorithm. We show numerically that our proposed method can effectively approximate the minimum of a function even if it is nonsmooth or discontinuous. We also introduce partitioning to estimate the global minimum of multimodal functions. Furthermore, we compare the performance of SGS with Simulated Annealing in estimating the global minimum of a set of multimodal functions. Lastly, we apply our method to estimate the parameters of a physiological system.