Numerical experiments with the one-dimensional non-linear simplex search

20 different functions have been used to test the 1-D simplex search algorithm in multi-dimensional optimization with Powell’s method. It was found that the simplex algorithm would converge fast if the values of parameters α, β, and δ are chosen such that 0<β•0.5 and 1•(α+δ)•1.2. The exact values being dependent on the function structure. In comparison with other 1-D methods, the simplex search requires, on average, a greater number of function evaluations than quadratic interpolation; it is, however, more efficient than the Fibonnaci search when used for line searches in a multi-dimensional minimizing method.