Generating Set Search Methods for Piecewise Smooth Problems

We consider a direct search approach for solving nonsmooth minimization problems where the objective function is locally Lipschitz continuous and piecewise continuously differentiable on a finite family of polyhedra. A generating set search method is proposed, which is named structured because the structure of the set of nondifferentiability near the current iterate is exploited to define the search directions at each iteration. Some numerical results are presented to validate the approach.