Based on the notation of Mordukhovich subdifferentials (Mordukhovich in Variational analysis and generalized differentiation I: basic theory, Springer, Berlin, 2006; Variational analysis and generalized differentiation II: applications, Springer, Berlin, 2006; Variational analysis and applications, Springer, Berlin, 2018), we establish strong Karush–Kuhn–Tucker type necessary optimality conditions for the weak efficiency of a nonsmooth nonconvex multiobjective programming problem with set, inequality and equality constraints. We also provide several new definitions for the Mordukhovich-pseudoconvexity and Mordukhovich-quasiconvexity with extended-real-valued functions, and then provide sufficient optimality conditions for weak efficiency to such problem in terms of Mordukhovich subdifferentials.

基于Mordukhovich次微分的表示法（Mordukhovich在变分分析和广义微分I：基本理论，施普林格，柏林，2006;变分分析和广义微分II：应用，施普林格，柏林，2006;变分分析和应用，Springer，柏林， 2018年），我们建立了具有集，不等式和等式约束的非光滑非凸多目标规划问题的弱效率的强Karush-Kuhn-Tucker类型必要最优条件。我们还提供了具有扩展实值函数的Mordukhovich-伪凸和Mordukhovich-拟凸的几个新定义，然后根据Mordukhovich次微分为此类问题的弱效率提供了充分的最优条件。