In this paper, the robust approach (the worst case approach) for nonsmooth nonconvex optimization problems with uncertainty data is studied. First various robust constraint qualifications are introduced based on the concept of tangential subdifferential. Further, robust necessary and sufficient optimality conditions are derived in the absence of the convexity of the uncertain sets and the concavity of the related functions with respect to the uncertain parameters. Finally, the results are applied to obtain the necessary and sufficient optimality conditions for robust weakly efficient solutions in multiobjective programming problems. In addition, several examples are provided to illustrate the advantages of the obtained outcomes.

本文研究了具有不确定性数据的非光滑非凸优化问题的鲁棒方法（最坏情况方法）。首先基于切向次微分的概念引入各种鲁棒约束条件。此外，在不确定集合的凸性和相关函数相对于不确定参数的凹性不存在的情况下，得出了鲁棒的必要条件和充分的最优条件。最后，将结果应用于获得多目标规划问题中健壮的弱有效解的必要和充分的最优条件。此外，提供了一些示例来说明所获得结果的优势。