Relationships Between Polyhedral Convex Sets and Generalized Polyhedral Convex Sets
Relationships Between Polyhedral Convex Sets and Generalized Polyhedral Convex Sets
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DOI：
10.1007/s10957-023-02269-2
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发表时间：
2022-12
影响因子：
1.9
通讯作者：
Nguyen Ngoc Luan;N. M. Nam;N. N. Thieu-N.;N. D. Yen
中科院分区：
文献类型：
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作者：
Nguyen Ngoc Luan;N. M. Nam;N. N. Thieu-N.;N. D. Yen
本文研究了多面体凸集与广义多面体凸集之间的关系。特别地，我们通过一个反例澄清了Ng et al. （Nonlinear Anal. 55:845-858, 2003; Theorem 3.1）得到的凸集与多面体凸集分离的充分必要条件在考虑广义多面体凸集而不是多面体凸集时不再有效。介绍并研究了广义多面体多函数和由广义多面体凸多函数生成的最优值函数的概念及其广义微分演算规则。
In this paper, we study some relationships between polyhedral convex sets and generalized polyhedral convex sets. In particular, we clarify by a counterexample that the necessary and sufficient conditions for the separation of a convex set and a polyhedral convex set obtained by Ng et al. (Nonlinear Anal. 55:845–858, 2003; Theorem 3.1) are no longer valid when considering generalized polyhedral convex sets instead of polyhedral convex sets. We also introduce and study the notions of generalized polyhedral multifunctions and optimal value functions generated by generalized polyhedral convex multifunctions along with their generalized differentiation calculus rules.