Golden Search Procedure

The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval.

Step 1. Pick up the two points c = a + (1 − r)h and d = a + rh inside the interval [a, b], where r = (√5 − 1)/2 and h = b − a.
Step 2. If the values of f (x) at the two points are almost equal [i.e., f (a) ≈ f (b)] and the width of the interval is sufficiently small (i.e., h ≈ 0), then stop the iteration to exit the loop and declare xo = c or xo = d depending on whether f (c) < f (d) or not. Otherwise, go to Step 3.
Step 3. If f (c) < f (d), let the new upper bound of the interval b ← d; otherwise, let the new lower bound of the interval a ← c. Then, go to
Step 1.

Reference:
Applied Numerical Methods Using MATLAB®
Author(s): Won Young Yang, Wenwu Cao, Tae‐Sang Chung, John Morris
First published:14 January 2005
Print ISBN:9780471698333 |Online ISBN:9780471705192 |DOI:10.1002/0471705195
Copyright © 2005 John Wiley & Sons, Inc