Derivative-free methods for mixed-integer nonsmooth constrained optimization

Abstract In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, scheme for bound combines dense sequence directions nonsmoothness objective function with primitive discrete variables described. Then, an exact penalty approach embedded in manage nonlinear (possibly nonsmooth) constraints. Global convergence properties algorithms toward stationary points analyzed and results extensive numerical experience on set test reported.