Minimizes a function via the Fibonacci method (direct search technique). The Fibonacci numbers can be computed by: F_n = (pⁿ − mⁿ) ⁄ √5, with (p, m) = (1 ± √5) ⁄ 2. The functions are:

1. y = (x − 0.5)² + 1 (solution, x = 0.5, y = 1)
2. y = x² − sinx (sol., x = 0.4501, y = -0.2324...)
3. y = x² + 2x (sol., x = -1, y = -1: from (-3, 5), reduce to 0.2, giving (-0.963636, -0.998678) [Baz. & Sh., 1993])

The graph shows y or the evolution of the minimization vs. the iteration step.

• Bazaraa, M. S., C. M. Shetty, 1993, "Non-linear Programming: theory and algorithms", 2.nd ed., Wiley.

• Weisstein, Eric W., "Binet's Fibonacci number formula". From MathWorld—A Wolfram Web Resource.

• 1622-07-04: Sluze, René François Walter de (1685-03-19).