Over the past thirty years there has been a growing need and interest for nonsmooth optimization methods. At the same time there has been an enormous research activity in nonsmooth analysis, where the classical derivative concepts have been extended to certain classes of Lipschitz continuous functions. Much of this very sophisticated theory has yet to be implemented and communicated to users of optimization algorithms. In the summer school international experts will present optimality conditions and algorithms for solving nonsmooth optimization problems more efficiently than by simple sampling methods. The School will contribute to the consolidation of a Latin American network on Optimization and Control. It will be addressed to postgraduate students and young researchers wishing to enrich and deepen their knowledge in the field of applied mathematics.