  The key element of the approach to the theory of necessary conditions in
optimal control discussed in the paper is reduction of the original constrained
problem to unconstrained minimization with subsequent application of a suitable
mechanism of local analysis to characterize minima of (necessarily nonsmooth)
functionals that appear after reduction. Using unconstrained minimization at
the crucial step of obtaining necessary conditions definitely facilitates
studies of new phenomena and allows to get more transparent and technically
simple proofs of known results. In the paper we offer a new proof of the
maximum principle for a nonsmooth optimal control problem (in the standard
Pontryagin form) with state constraints and then prove a new second order
condition for a strong minimum in the same problem but with data differentiable
with respect to the state and control variables. The role of variational
analysis is twofold. Conceptually, the main considerations behind the reduction
are connected with metric regularity and Ekeland's principle. On the other
hand, technically, calculation of subdifferentials of components of the
functionals that appear after the reduction is an essential part of the proofs.
