Set-valued extensions of vector-valued functions are used to investigate the relations between weak efficiency and variational inequalities (both Stampacchia and Minty type) which allows to apply the complete lattice framework from set optimization. Since the seminal work of Giannessi, it has been a challenge to generalize scalar results to the vector case. In this effort, some notions of generalized derivatives for vector-valued functions have been introduced, either in the form of set-valued functions or introducing appropriate notions of infinite elements in vector spaces. Switching the focus to set optimization in conlinear spaces, we propose a Dini-type derivative, that keeps the same set-valued form of the optimization problem.

中文翻译：

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将集合优化应用于弱效率

向量值函数的集值扩展用于研究弱效率和变分不等式（Stampacchia 和 Minty 类型）之间的关系，这允许应用来自集合优化的完整格框架。自从 Giannessi 的开创性工作以来，将标量结果推广到向量案例一直是一个挑战。在这项工作中，已经引入了向量值函数的广义导数的一些概念，以集值函数的形式或引入向量空间中无限元素的适当概念。将焦点切换到共线性空间中的集合优化，我们提出了 Dini 型导数，它保持优化问题的相同集合值形式。