Optimality of Interval Reduction in the Golden Section Search Method

Students often conflate the reduction factor

\rho \approx 0.618

with the golden ratio

\phi \approx 1.618

. Remember:

\rho = 1/\phi

. The interval shrinks by

0.618

of its previous size, meaning

38.2\%

of the search space is discarded each iteration.

Institutional Reference: Fundamentals of Optimization