Search Strategy - Fibonacci Search

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Search Strategy

The strategy described here, the method is extremely simple.
Basis for the simplified algorithm was the idea to avoid the determination of the various intervals. There were the distances between the various examined points determined. As a result was found a very simple relationship.
Consider the interval to be examined [a, b]. The number of search steps is m. Furthermore, we assume that a minimum should be searched.
In this interval, the first two points to be examined are

The distances of x1 to the left interval boundary and x2 to the right interval boundary are equal.
In our considerations, we start the calculation from the left interval boundary a.
The distance between the first search point and a is

For the distance of the second search point from the first one follows

Depending on which of the points of minor functional value occurs, it is as a starting point
taken for the following search step.

Other considerations, which will not be discussed in detail here showed the distance of the third Point
from the previous search to

Generally follows the step width of the k-th search step to

Now the search direction must only be determined.
The search direction remains unchanged as a function value smaller than the previous one, otherwise it is changed.

This is the basis of a flow chart for the one-dimensional Fibonacci search algorithm like shown on the
next page. It is so simple, so that the extension to higher dimensions is not a problem.

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