Variational Analysis in the light of Tame Geometry


Il giorno 28 febbraio alle ore 12.15 in aula 1AD/30 il prof. Aris Daniilidis dell'Universita' Autonoma di Barcellona terra' un seminario dal titolo "Variational Analysis in the light of Tame Geometry".

- Abstract
In considering the minimization of a nonsmooth function it has been noted that, in general, the minimum occurs at a point of nondifferentiability. It has also been noted however, that nonsmoothness seldom occurs in a random manner, but instead, has an underlying structure which can be exploited in optimization. This underlying structure
often appears to take the form of a manifold along which the function appears smooth, but away from which the function appears nonsmooth. The central idea in this talk is to relate derivative ideas from two distinct mathematical sources: variational analysis and tame geometry. Specifically, we are interested in a particular class of well-structured nonsmooth functions, namely functions admitting a Whitney stratification. This class contains in
particular functions that are definable in some o-minimal structure, so the derived results can directly be applied in several concrete optimization problems involving for example a semi-algebraic or a subanalytic structure.

Rif. G. Colombo, F. Rampazzo