On a possible generalization of Pshenichnyi’s quasidifferentiability

Applying some results of J.-P. Crouzeix 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 generalized upper quasidifferentiable function is formulated and the steepest normalized descent direction for a regular generalized upper quasidifferentiable function is determined.