This work considers nonsmooth and nonconvex optimization problems whose objective and constraint functions are defined by difference-of-convex (DC) functions. We consider an infeasible bundle method based on the so-called improvement functions to compute critical points for problems of this class. Our algorithm neither employs penalization techniques nor solves subproblems with linearized constraints. The approach, which encompasses bundle methods for nonlinearly-constrained convex programs, defines trial points as solutions of strongly convex quadratic programs. Different stationarity definitions are investigated, depending on the functions’ structures. The approach is assessed in a class of nonsmooth DC-constrained optimization problems modeling chance-constrained programs.

这项工作考虑了非光滑和非凸优化问题，其目标函数和约束函数由凸差（DC）函数定义。我们考虑一种基于所谓的改进函数的不可行捆绑方法来计算此类问题的关键点。我们的算法既没有采用惩罚技术，也没有解决带有线性约束的子问题。该方法包括用于非线性约束凸程序的捆绑方法，该方法将试验点定义为强凸二次程序的解。根据功能的结构，研究了不同的平稳性定义。该方法在建模机会受限程序的一类非平滑直流受限优化问题中进行了评估。