We describe an extension of the classical cutting plane algorithm to tackle the unconstrained minimization of a nonconvex, not necessarily differentiable function of several variables. The method is based on the construction of both a lower and an upper polyhedral approximation to the objective function and is related to the use of the concept of proximal trajectory. Convergence to a stationary point is proved for weakly semismooth functions.

The paper describes a model for the optimal management of periodic deliveries of a given commodity. The goal is to schedule the deliveries according to feasible combinations of delivery days and to determine the scheduling and routing policies of the vehicles in order to minimize over the planning horizon the maximum number of vehicles simultaneously employed, i.e., the fleet size. Heuristic algorithms are proposed and computational experience is reported.

We introduce an algorithm to minimize a function of several variables with no convexity nor smoothness assumptions. The main peculiarity of our approach is the use of an objective function model which is the difference of two piecewise affine convex functions. Bundling and trust region concepts are embedded into the algorithm. Convergence of the algorithm to a stationary point is proved and some numerical results are reported.