Among applications of variational analysis to optimization one of the most important is connected with the possibility to equivalently reduce constrained problems to unconstrained minimization of sufficiently well organized functionals. It opens doors to a fairly new approach to the study of necessary optimality conditions. In optimal control the unconstrained problems look like Bolza problems of calculus of variations with, necessarily, nonsmooth integrand and off-integral term. But the analysis of such problems in many respects is much simpler.
In the talk I shall briefly describe how this approach works for a proof of the Pontryagin maximum principle and then discuss with some more details a new second order condition for a strong minimum. I hope also to mention some open problems, if time permits.