On a possible generalization of pshemchhy's quasidifferentiability

Applying some results of J.-P. Cbouzeix the notion of quasidifferentiability of a function due to B. N. PSHENICHNYI is generalized and a quasisubdifferential is defined for generalized upper quasidifferentiable functions. By the help of the quasisubdifferential a necessary condition for local minima of a generalised upper qusidifferentiable function is formulated and the steepest normalizes desecent direction for a regular generalized upper quasidifferentiable function is determined.