The notion of a normal cone of a given set is paramount in optimization and variational analysis. In this work, we give a definition of a multiobjective normal cone, which is suitable for studying optimality conditions and constraint qualifications for multiobjective optimization problems. A detailed study of the properties of the multiobjective normal cone is conducted. With this tool, we were able to characterize weak and strong Karush–Kuhn–Tucker conditions by means of a Guignard-type constraint qualification. Furthermore, the computation of the multiobjective normal cone under the error bound property is provided. The important statements are illustrated by examples.

给定集合的法线圆锥的概念在优化和变分分析中至关重要。在这项工作中，我们给出了一个多目标法线锥的定义，该定义适用于研究多目标优化问题的最优性条件和约束条件。对多目标法线锥的性质进行了详细研究。使用该工具，我们能够通过吉格纳型约束条件来描述弱和强Karush–Kuhn–Tucker条件。此外，提供了在误差限制属性下的多目标法线锥的计算。重要的陈述通过示例进行说明。