An extension of golden section algorithm for n-variable functions with MATLAB code

Golden section search method is one of the fastest direct search algorithms to solve single variable optimization problems, in which the search space is reduced from [a, b] to [0,1]. This paper describes an extended golden section search method in order to find the minimum of an n-variable function by transforming its n-dimensional cubic search space to the zero-one n-dimensional cube. The paper also provides a MATLAB code for two-dimensional and three-dimensional golden section search algorithms for a zero-one n-dimensional cube. Numerical results for some benchmark functions up to five dimensions and a comparison of the proposed algorithm with the Neldor Mead Simplex Algorithm is also provided.