Minimizing nonconvex nonsmooth functions via cutting planes and proximity control

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.