Nonlinear Opt.: Gold section search 1

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Interval reduction methods usually use the function value of two interior points in the interval to decide the direction in which to reduce it. One elegant way is to recycle one of the evaluated points and to use it in the next iterations. This can be done by using the so-called Golden Section rule. This method uses two evaluated points l (left) and r (right) in the interval [ak, bk], that are located in such a way that one of the points can be used again in the next iteration. The idea is sketched in Figure 5.1. The evaluation points l and r are located with fraction τ in such a way that l = a+(1−τ )(b−a) and r = a + τ (b − a).