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Fibonacci method
Minimizes a function via the Fibonacci method.
2025.Feb.19 21:27:47
Function     Function to minimize. •
xleft, xright Search interval.
reduce to Reduced final interval (in minimization). •
iprt Intermediate steps.
Graph   Graphs: function or minimization evolution. •
Show values ? Shows the graph coordinates.

Minimizes a function via the Fibonacci method (direct search technique). The Fibonacci numbers can be computed by: Fn = (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.

References: Plate: Fibonacci

• 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).

 
 
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Created: 2010-07-04 — Last modified: 2018-11-11