NUMERICAL EXPERIMENTS WITH THE ONE-DIMENSIONAL NONLINEAR SIMPLEX SEARCH

We have used 20 different functions 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 alpha, beta, and delta are chosen such that 0 < beta less-than-or-equal-to 0.5 and 1 less-than-or-equal-to (alpha + delta) less-than-or-equal-to 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.