In practical applications of optimization we often get into the situation where the objective function to be minimized/maximized is not necessarily differentiable. The source of the nonsmoothness may be the objective function itself, its possible interior function or both. For example, economics tax models typically consists of several different elements which at their intersections have discontinuous gradients. In optimal control problems governed by partial differential systems the smoothness may be caused by the technological constraints. We may add that there also exist so called stiff problems which are smooth analytically but nonsmooth numerically, where the gradient varies too rapidly and the classical methods will fail. Thus we cannot directly use the methods demanding differential information while the usual methods that do not require gradients are often very inefficient. Instead of gradients we must use the so called generalized gradients (or subgra- dients) which allow us to generalize the effective smooth derivative methods for nonsmooth problems.