Basic Idea
The diagram above illustrates a single step in the technique for finding a minimum. The functional values of are on the vertical axis, and the horizontal axis is the x parameter. The value of has already been evaluated at the three points:, and . Since is smaller than either or, it is clear that a minimum lies inside the interval from to (since f is unimodal).
The next step in the minimization process is to "probe" the function by evaluating it at a new value of x, namely . It is most efficient to choose somewhere inside the largest interval, i.e. between and . From the diagram, it is clear that if the function yields then a minimum lies between and and the new triplet of points will be, and . However if the function yields the value then a minimum lies between and, and the new triplet of points will be, and . Thus, in either case, we can construct a new narrower search interval that is guaranteed to contain the function's minimum.
Read more about this topic: Golden Section Search
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