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Philip D. Loewen:
Applications to Optimal Control

I will discuss the Generalized Problem of Bolza, in which a given
integral functional is to be minimized over some subset of the class of
absolutely continuous functions carrying the real interval [0,1] into a
finite-dimensional Euclidean space. In the absence of differentiability,
the classical Calculus of Variations provides guidance about the general
appearance of results one should expect. However, the precise
formulation of suitable nonsmooth extensions and the techniques required
to prove them make essential use of recent developments in nonsmooth
analysis. These lectures will treat, in varying levels of detail,
problem formulation, necessary conditions for optimality, sufficient
conditions for optimality, and optimal feedback control.