Colloquium Mathematics, Professor Terry Rockafellar

Join us for coffee and tea at 15.30 p.m.

Title: Variational Analysis, Variational Geometry, and Optimization

Abstract:

Classical analysis covers many function-constructing operations, such as
addition, multiplication, composition and even integration, but not the
operations that are essential in optimization, namely minimization and
maximization.   The simple reason is that those operations don't preserve
differentiability.  If a function g(x) is defined as the minimum (or the
maximum) of f(x,y) with respect to y in some set Y, no amount of
differentiability of f in x and y will carry over, in general, to g being
differentiable in x.

Variational analysis, as an extension of classical analysis which encompasses
also convex analysis, gets around this by introducing one-sided concepts of
generalized differentiability which moreover have a basis in set convergence
very different from the usual pointwise convergence of different quotients.  
Variational geometry provides powerful support by associating one-sided tangent
and normal "cones" instead of subspaces to the points of a set in a linear space.  
Novel concepts of regularity, unanticipated in classical theory, then come up.

This talk will aim at explaining these ideas on broad introductory level.

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and
Dr. A.V. Kiselev (e-mail: a.v.kiselev@rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/