One-dimensional unconstrained optimization is used to minimize the function of the type . The golden section search method is a zero-line search method used to solve functions of the type . This method uses the values of the objective function f and not their derivatives, making this type of solution best applicable to minimize the function since f(x) is not differentiable at x = 2.5.

The golden section search method

The golden section search method uses an interval reduction strategy independent of the number of iterations, where the ratio between the sizes of two consecutive intervals is constant and makes use of the golden ratio . The golden ratio is defined algebraically as follows:

Here, .

Basically, it is an iterative method that minimizes the function by:

• Defining an interval [a, b] that contains the minimizer.

• Shrinking the interval into progressively smaller intervals [a', b'] that still contain the minimizer.

• Repeating the second step until the difference...