Higher Order Weak Sharp Minima With An Arbitrary Non-differentiable Function

In this paper,we study higher order weak sharp minima of a given non-differentiable function.First,we give a necessary condition for the existence of higher order weak sharp minima by using lower Hadamard directional derivative and lower Hadamard subdifferential.Then,we define a new directional derivative,which is called Hadamard-Clarke directional derivative,and give a sufficient condition for the existence of higher order weak sharp minima in terms of it.Next,we study the relationship between higher order local weak sharp minima and globle weak sharp minima.Finally,we give a method to determine minimum order n weak sharp minima.