A bundle–Newton method for nonsmooth unconstrained minimization

An algorithm based on a combination of the polyhedral and quadratic approximation is given for finding stationary points for unconstrained minimization problems with locally Lipschitz problem functions that are not necessarily convex or differentiable. Global convergence of the algorithm is established. Under additional assumptions, it is shown that the algorithm generates Newton iterations and that the convergence is superlinear. Some encouraging numerical experience is reported.