A fast gradient and function sampling method for finite-max functions

This paper proposes an algorithm for the unconstrained minimization of a class of nonsmooth and nonconvex functions that can be written as finite-max functions. A gradient and function-based sampling method is proposed which, under special circumstances, either moves superlinearly to a minimizer of the problem of interest or improves the optimality certificate. Global and local convergence analysis are presented, as well as examples that illustrate the obtained theoretical results.