AN ALGORITHM FOR MINIMIZING A DIFFERENTIABLE FUNCTION THAT USES ONLY FUNCTION VALUES

Abstract

The problem is to determine whether or not there exists a neighborhood of a given point in which
a real-valued function of real-variables can be accurately approximated by a quadratic function.
As such, this paper explores a better way to determine the local minimal point of the given
function based on some critical assumptions and the algorithm that utilizes only function values.
The result of the experiments show that MR1 with either search A or search C should be used
because the terminal convergence is superior to that of the rank 2 schemes and the number of
function evaluations required is only about half that required by Powell’s no derivative scheme.