This paper is devoted to the investigation of optimality conditions for approximate quasi weak efficient solutions for a class of vector equilibrium problem (VEP). First, a necessary optimality condition for approximate quasi weak efficient solutions to VEP is established by utilizing the separation theorem with respect to the quasirelative interior of convex sets and the properties of the Clarke subdifferential. Second, the concept of approximate pseudoconvex function is introduced and its existence is verified by a concrete example. Under the assumption of introduced convexity, a sufficient optimality condition for VEP in sense of approximate quasi weak efficiency is also presented. Finally, by using Tammer’s function and the directed distance function, the scalarization theorems of the approximate quasi weak efficient solutions of the VEP are proposed.

中文翻译：

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向量平衡问题的近似拟弱有效解的最优性条件和标化

本文致力于一类矢量平衡问题（VEP）的近似拟弱有效解的最优性条件的研究。首先，利用关于凸集的拟相对内部的分离定理和Clarke次微分的性质，为VEP的近似拟弱有效解建立了必要的最优性条件。其次，介绍了近似伪凸函数的概念，并通过一个具体实例验证了其存在性。在引入凸度的假设下，从近似准弱效率的角度给出了VEP的充分最优条件。最后，通过使用Tammer函数和有向距离函数，