Topic 14. Optimization

3. Method of golden section

The gold section of the segment is called its division into two parts, that the ratio of the length of the entire segment to the length of most part is equal to the ratio of the length of the greater part to the smaller. So the gold section of the segment [] performs two symmetrically arranged points, where k = 0.6180339. That is, the point x ₁ divides the segment [ a , x ₂ ] in the golden ratio , and the point x ₂ is the gold section of the segment [ x ₁ , b ] .

In the golden section method, the function must be unimodal. The function is unimodal on a segment if it has a single point of the global minimum on this segment and to the left of this point is strictly decreasing, and to the right is strictly increasing. The essence of the golden section method is to determine the point of the global minimum for a segment for a minimum number of steps.