A Characterization of Paratingent Cone and P-subderivative with Applications in Nonsmooth Analysis

We give a new characterization of the paratingent cone in terms of contingent cones. i.e.. the paratingent cone to any open set at a boundary point is the upper limit of the contingent cones at the neighboring points. We use this result to characterize the strict differentiability in terms of the contingent directional derivatives. We also define a Psubderivative for continuous functions and develop a subdifferential calculus with applications to optimality conditions in mathematical programming.