On the basis of the notion of approximating family of cones and a generalized type of Gerstewitz’s/Tammer’s nonlinear scalarization functional, we establish variants of the Ekeland variational principle (for short, EVP) involving set perturbations for a type of approximate proper solutions in the sense of Henig of a vector equilibrium problem. Initially, these results are obtained for both an unconstrained and a constrained vector equilibrium problem, where the objective function takes values in a real locally convex Hausdorff topological linear space. After that, we consider special cases when the objective function takes values in a normed space and in a finite-dimensional vector space. For the finite-dimensional objective space with a polyhedral ordering cone, we give the explicit representation of variants of EVP depending on matrices, and in such a way, some selected applications for multiobjective optimization problems and vector variational inequality problems are also derived.

根据近似锥族的概念和广义类型的Gerstewitz / Tammer的非线性标量函数，我们建立了Ekeland变分原理（简称EVP）的变体，其中涉及到设置扰动，表示某种意义上的近似正确解向量平衡问题的Henig的概念。最初，这些结果是针对无约束和有约束的矢量平衡问题获得的，其中目标函数采用实际的局部凸Hausdorff拓扑线性空间中的值。之后，我们考虑特殊情况，即目标函数在赋范空间和有限维向量空间中取值。对于具有多面体有序锥的有限维目标空间，我们根据矩阵给出EVP变体的显式表示，