The definitions of the relative derivatives of a tensor with respect to time in any reference frame by using the notation of vectrix were proposed.

This article profoundly revealed the reference system problem in momentum dotand momentum parameters cd the "dot complex motion"; and the absolutederivative and relative derivative for any variable vector and K s accelerationproblem, etc.

The optimization problem of the set valued map with the contingent derivative and the tangent derivative of the set valued map is discussed, and the Kuhn Tucker necessary optimality condition and sufficient optimality conditions under the assumption of the cone convexity are give

In this paper,we obtain the necessary conditions,the sufficient conditions,the necessary and sufficient conditions at the Lagrange multipliers status for weak minimizer solution to the set-valued optimization problems by using the contingent derivative,the adjacent derivative and the circatangent derivative.

In terms of the contingent derivative,some equivalent conditions on the existence of an error bound for pseudoconvex multifunctions are established.

In this paper,the existence of solution to the variational inclusions concerning intermediate derivatives is discussed in the Banach space.

By view of these notions and the scalar derivatives,solution existence of variational inequalities are studied.