Tame Functions and Variational Analysis

All non-trivial theorems of local variational analysis applied to generic
non-differential functions (e.g. optimization problems with generic
Lipschitz data) produce not very informative, often just trivial
results. Fortunately, functions that usually appear in applications
have some special structures (e.g. polyhedral, linear-quadratic, spline
etc.). Typically such structures are particular cases of semi-algebraic
(or more generally, tame) structures. The latter turn out to be perfectly
compatible with basic constructions of local variational analysis which
excludes any possibility for the mentioned unpleasant phenomena to happen.
Moreover, in this case a number of powerful results can be proved that
are not otherwise valid.
The latter statements will be clarified in the talk, both in general terms
and for some important classes of problems, including standard problems of
mathematical programming, gradient dynamical systems and optimal control
of state-linear systems.