This paper generalizes and unifies different recent results as well as provides a new methodology concerning vector optimization problems involving composite mappings in locally convex Hausdorff topological vector spaces. The Lagrangian and weak Lagrangian dual problems are proposed. Characterizations of strong duality results are proved at the same time with characterizations of Farkas lemmas for composite vector mappings in a general setting (i.e. without any assumptions on convexity or continuity of the mappings involved). Corresponding results in the convex setting are also proposed by establishing as main tools some variants of representations of epigraphs of conjugate mappings in our composite vector framework. As by-products, several Farkas-type results for composite vector functions are proposed, which extend and cover several known ones recently appeared in the literature. Lastly, the results are applied to get duality results for a class of convex semi-vector bilevel optimization problems.

本文概括和统一了最近的不同结果，并提供了一种新的方法，涉及向量优化问题，涉及局部凸 Hausdorff 拓扑向量空间中的复合映射。提出了拉格朗日和弱拉格朗日对偶问题。强对偶结果的特征与一般环境中复合向量映射的 Farkas 引理的特征同时被证明（即，对所涉及的映射的凸性或连续性没有任何假设）。通过在我们的复合向量框架中建立作为主要工具的共轭映射的题词表示的一些变体，还提出了凸设置中的相应结果。作为副产品，提出了复合向量函数的几种 Farkas 型结果，它扩展并涵盖了最近出现在文献中的几个已知的。最后，将结果应用于一类凸半向量双层优化问题的对偶结果。