Join us for coffee and tea at 15.30 p.m.
Tuesday, June 17th 2014
Professor Terry Rockafellar,
University of Washington
Variational Analysis, Variational Geometry, and Optimization
Classical analysis covers many function-constructing operations, such asaddition, multiplication, composition and even integration, but not theoperations that are essential in optimization, namely minimization andmaximization. The simple reason is that those operations don't preservedifferentiability. If a function g(x) is defined as the minimum (or themaximum) of f(x,y) with respect to y in some set Y, no amount ofdifferentiability of f in x and y will carry over, in general, to g beingdifferentiable in x.
Variational analysis, as an extension of classical analysis which encompasses
also convex analysis, gets around this by introducing one-sided concepts ofgeneralized 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:
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