Relationships Between Polyhedral Convex Sets and Generalized Polyhedral Convex Sets
Sponsor
Research of this author was partly supported by the USA National Science Foundation under grantDMS-2136228. Research of Nguyen Ngoc Luan and Nguyen Dong Yen was funded by the Vietnam Ministryof Education and Training under grant number B2022-CTT-06.
Published In
Journal of Optimization Theory and Applications
Document Type
Citation
Publication Date
7-18-2023
Abstract
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 (Nonlinear Anal. 55:845–858, 2003; Theorem 3.1) are no longer valid when considering generalized polyhedral convex sets instead of polyhedral convex sets.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.
Rights
© The Author(s)
Locate the Document
DOI
10.1007/s10957-023-02269-2
Persistent Identifier
https://archives.pdx.edu/ds/psu/40693
Publisher
Springer Nature
Citation Details
Luan, N. N., Nam, N. M., Thieu, N. N., & Yen, N. D. (2023). Relationships between polyhedral convex sets and generalized polyhedral convex sets. Journal of Optimization Theory and Applications, 1-21.