Orateur
Description
Identifying Blaschke-Santal´o diagrams is an important topic that
essentially consists in determining the image Y = F (X) of a map F : X →
Rd, where the dimension of the source space X is much larger than the
one of the target space. In some cases, that occur for instance in shape
optimization problems, X can even be a subset of an infinite-dimensional
space. The usual Monte Carlo method, consisting in randomly choosing a
number N of points x1, . . . , xN in X and plotting them in the target
space Rd, produces in many cases areas in Y of very high and very low
concentration leading to a rather rough numerical identification of the
image set. On the contrary, our goal is to choose the points xi in an
appropriate way that produces a uniform distribution in the target
space. In this way we may obtain a good representation of the image set
Y by a relatively small number N of samples which is very useful when
the dimension of the source space X is large (or even infinite) and the
evaluation of F (xi) is costly.
Joint work with BENIAMIN BOGOSEL, GIUSEPPE BUTTAZZO
