  Construction of an united theory of the subdifferentials of the first and
second orders is interesting for many specialists in optimization
\cite{morduchrockafel}. In the paper the rules for construction of the
subdifferentials of the first and second orders are introduced. The
constructions are done with the help of the Steklov integral of a Lipschitz
function $f(\cdot)$ over the images of a set-valued mapping $D(\cdot)$. It is
proved that the subdifferential of the first order consisting of the average
integral limit values of the gradients $\nabla f(r(\cdot))$, calculated along
the curves $r(\cdot)$ from an introduced set of curves $\eta$, coincides with
the subdifferentials of the first order constructed using the Steklov integral
introduced by the author for the first time in \cite{lowapp2}, \cite{lowapp2a}.
If the function $f(\cdot)$ is twice differentiable at $x$ then the
subdifferentials of the first and second orders coincide with the gradient
$\nabla f(r(\cdot))$ and the matrix of the second mixed derivatives of
$f(\cdot)$ at $x$. The generalized gradients and matrices are used for
formulation of the necessary and sufficient conditions of optimality. The
calculus for the subdifferentials of the first and second orders is
constructed. The examples are given.
