Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets
研究了约束包含非光滑非凸函数和闭集交的鲁棒优化问题，利用变分分析给出了最优性的必要和充分条件，并建立了对偶问题及对偶关系。
Abstract In this paper, we study a robust optimization problem whose constraints include nonsmooth and nonconvex functions and the intersection of closed sets. Using advanced variational analysis tools, we first provide necessary conditions for the optimality of the robust optimization problem. We then establish sufficient conditions for the optimality of the considered problem under the assumption of generalized convexity. In addition, we present a dual problem to the primal robust optimization problem and examine duality relations.