In this paper, we give necessary conditions for the existence of a strict local minimum of order two for multiobjective optimization problems with equality and inequality constraints. We suppose that the objective function and the active inequality constraints are only locally Lipschitz. We consider both regular equality constraints and degenerate equality constraints. This article could be considered as a continuation of [E. Constantin, Necessary Conditions for Weak Efficiency for Nonsmooth Degenerate Multiobjective Optimization Problems, J. Global Optim, 75, 111-129, 2019]. We introduce a constraint qualification and a regularity condition, and we show that under each of them, the dual necessary conditions for a weak local minimum of the aforementioned article become of Kuhn-Tucker type.

在本文中，我们给出了存在等式和不等式约束的多目标优化问题存在严格的二阶局部极小值的必要条件。我们假设目标函数和主动不等式约束只是局部的Lipschitz。我们同时考虑规则相等约束和退化相等约束。本文可以视为[E. Constantin，非光滑退化多目标优化问题弱效率的必要条件，J。Global Optim，75，111-129，2019]。我们介绍了一个约束条件和一个正则条件，并且我们证明了在每种条件下，上述物品的弱局部极小值的双重必要条件成为Kuhn-Tucker类型。