SIAM Journal on Optimization, Volume 31, Issue 1, Page 837-865, January 2021.
This paper deals with particular families of DC optimization problems involving suprema of convex functions. We show that the specific structure of this type of function allows us to cover a variety of problems in nonconvex programming. Necessary and sufficient optimality conditions for these families of DC optimization problems are established, where some of these structural features are conveniently exploited. More precisely, we derive necessary and sufficient conditions for (global and local) optimality in DC semi-infinite programming and DC cone-constrained optimization, under natural constraint qualifications. Finally, a penalty approach to DC abstract programming problems is developed in the last section.

中文翻译：

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DC半无限规划的充要条件

SIAM优化杂志，第31卷，第1期，第837-865页，2021年1月。
本文讨论了涉及凸函数极值的特殊DC优化问题系列。我们证明了这类函数的特定结构使我们能够解决非凸编程中的各种问题。建立了这些直流优化问题系列的必要和充分的最优条件，可以方便地利用其中的某些结构特征。更准确地说，我们在自然约束条件下为DC半无限编程和DC锥约束优化中的（全局和局部）最优性导出了充要条件。最后，在最后一部分中开发了一种针对DC抽象编程问题的惩罚方法。