The aim of this paper is to develop first-order necessary and sufficient optimality conditions for nonsmooth multiobjective optimization problems with vanishing constraints. First of all, we introduce some data qualifications for the problem, and derive the comparisons between them. Secondly, based on the mentioned qualifications, we demonstrate some necessary optimality conditions, named strongly stationary conditions, at weakly efficient and efficient solutions of considered problem. Then, we show that the strongly stationary conditions are also sufficient for optimality. Finally, using the tightened problems, we establish other classes of qualifications and stationary conditions.

本文的目的是为约束消失的非光滑多目标优化问题开发一阶必要和充分的最优条件。首先，我们介绍了该问题的一些数据限定条件，并得出了它们之间的比较结果。其次，基于上述限定条件，我们在考虑问题的弱有效解决方案中证明了一些必要的最优性条件，称为强平稳条件。然后，我们表明强静止条件也足以达到最优。最后，使用更严格的问题，我们建立了其他类别的资格和固定条件。