论文标题
多面体凸组与广义的多面体凸组之间的关系
Relationships between Polyhedral Convex Sets and Generalized Polyhedral Convex Sets
论文作者
论文摘要
在本文中，我们研究了多面体凸组（PC）与广义多面体凸组（GPC）之间的一些关系。特别是，我们通过反例澄清，在[Fenchel二重性中以有限维设置及其应用，非线性肛门而在功夫二元性中获得的凸组和PC的必要条件和PC。 55（2003），845--858;当考虑GPC而不是PC时，定理〜3.1]不再有效。我们还介绍并研究了广义的多面体设定值映射的概念和由广义的多面体凸set值映射产生的最佳价值函数及其广义分化演算规则。
In this paper we study some relationships between polyhedral convex sets (PCS) and generalized polyhedral convex sets (GPCS). In particular, we clarify by a counterexample that the necessary and sufficient conditions for the separation of a convex set and a PCS obtained by Kung Fu Ng and Wen Song in [Fenchel duality in finite-dimensional setting and its applications, Nonlinear Anal. 55(2003), 845--858; Theorem~3.1] are no longer valid when considering GPCS instead of PCS. We also introduce and study the notions of generalized polyhedral set-valued mappings and optimal value functions generated by generalized polyhedral convex set-valued mappings along with their generalized differentiation calculus rules.
