Technical Note—A Stopping Criterion for the Golden-Ratio Search

Abstract

This note presents a stopping criterion for the golden-ratio search for the optimum of a one-dimensional, unimodal function. Given ϵ, the minimum separation between two points such that the corresponding values of the function remain distinguishable, we show that the search should be terminated when the interval of uncertainty is less than ϵ p /(2 − p ), where p is the golden ratio.