Infinite Dimensional Clarke Generalized Jacobian

We extend for a locally Lipschitz function the notion of Clarke's generalized Jacobian to the setting where the domain lies in an infinite dimensional normed space. When the function is real-valued this notion reduces to the Clarke's generalized gradient. Using this extension, we obtain an exact smooth-nonsmooth chain rule from which the sum rule and the product rule follow. Also an exact formula for the generalized Jacobian of piecewise differentiable functions will be provided.