The " alpine " function

This function is defined by

In dimension two and on it gives the Figure 1. With a lot of imagination, you can almost recognize the French Côte d’Azur on the south and the Mont Blanc as the highest summit. This function is interesting for testing the search of an extremum for the following reasons:


Figure 1. The 2D alpine function.

In any dimension D, in the hypercube , the maximum is at the point  where xs is the solution of

that is to say the point . The maximal value is then about .                   1998/11/23