Extended Fibonacci search for proper sinusoidal functions

Abstract

Fibonacci search is a well-known one dimensional search technique used to optimize a unimodal function of one variable. It is optimal among all non-randomized search procedures with a given number of function evaluations in the sense that it yields the highest length ratio of beginning to ending interval of uncertainty. The purpose of this paper is to show that this property of optimality for a variation of the method, termed Extended Fibonacci Search, is preserved when it is applied to a class of functions which is more general than the unimodal class. This class is termed proper sinusoidal. The paper ends with a brief description of an application of this optimization approach to improve the efficiency of the TRANSYT traffic engineering computer program.