The main goal of this paper is to give some primal and dual Karush–Kuhn–Tucker second-order necessary conditions for the existence of a strict local Pareto minimum of order two for an inequality-constrained multiobjective optimization problem. Dual Karush–Kuhn–Tucker second-order sufficient conditions are provided too. We suppose that the objective function and the active inequality constraints are only locally Lipschitz in the primal necessary conditions and only strictly differentiable in sense of Clarke at the extremum point in the dual conditions. Examples illustrate the applicability of the obtained results.

中文翻译：

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局部 Lipschitz 不等式约束的多目标优化中的二阶最优性条件

本文的主要目标是为不等式约束的多目标优化问题存在严格的二阶局部帕累托最小值给出一些原始的和对偶的 Karush-Kuhn-Tucker 二阶必要条件。还提供了对偶 Karush-Kuhn-Tucker 二阶充分条件。我们假设目标函数和主动不等式约束仅在原始必要条件下局部 Lipschitz 并且仅在对偶条件极值点的 Clarke 意义上严格可微。实例说明了所得结果的适用性。