Generalized Directional Derivatives

Over the last fifty years, generalized second-order derivatives have been studied because it is important to state optimization conditions for nonsmooth functions. We recall e.g. the concept of convex subdifferential, the Clarke gradient for locally Lipschitz function or the co-derivatives studied by Boris Mordukhovich. In this book it was introduced the class of l-stable functions which is wider than the class of functions with locally Lipschitz gradient and there were stated some second-order optimization conditions. The characterization of convexity and strict convexity for locally Licpschitz functions is also provided. Moreover, a new characterization of minimal cusco is given.