广义Minty 向量似变分不等式解的性质

在拓扑向量空间中讨论下Dini方向导数形式的广义Minty向量似变分不等式问题. 可微形式的Minty变分不等式、Minty似变分不等式和Minty向量变分不等式是其特殊形式. 该文分别讨论了Minty向量似变分不等式的解与径向递减函数, 与向量优化问题的最优解或有效解之间的关系问题, 以及Minty向量似变分不等式的解集的仿射性质. 这些定理推广了文献中Minty变分不等式的一些重要的已知结果.

Properties of the Solution in Generalized Minty Vector Variational-like Inequalities

Generalized Minty vector variational-like inequalities as being of lower Dini directional derivative type are studied in topological vector  spaces, which include Minty variational inequalities, Minty  variational-like inequalities and Minty vector variational inequalities as being of differential type. Some relations between solutions of Minty vector variational-like inequalities and solutions of vector optimization problems, as well as radial decrease properties of functions, are investigated. Moreover, the affine solution sets of Minty  vector variational-like inequalities  are presented. As consequences, some recent known results in literature are obtained in the special case.