A Computer program to minimize a function with many variables using computer evaluated exact higher-order derivatives

摘要

This paper describes a computer program for an optimization algorithm using first- up to the rth-order derivatives to find the optimum of r-continuously-differentiable functions of many variables. The algorithm, developed by Kalaba and Tishler [6,7], obtains the exact values of the derivatives required for the optimization from the “table algorithm” presented in [4] and [5]. The optimization algorithm described here collapses to the well-known Newton–Raphson algorithm when only first- and second- order derivatives are used.