Derivative-free methods for mixed-integer nonsmooth constrained optimization
针对目标函数和约束函数仅能通过黑箱零阶预言机获取输出、不提供导数信息的混合整数非光滑约束优化问题，提出了一种新的无导数线搜索算法框架，并分析了全局收敛性。
Abstract In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are 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, a scheme for bound constrained problems that combines a dense sequence of directions to handle the nonsmoothness of the objective function with primitive directions to handle discrete variables is described. Then, an exact penalty approach is embedded in the scheme to suitably manage nonlinear (possibly nonsmooth) constraints. Global convergence properties of the proposed algorithms toward stationary points are analyzed and results of an extensive numerical experience on a set of mixed-integer test problems are reported.