A representation of generalized convex polyhedra and applications. (3rd March 2020)

• Record Type: Journal Article
• Authors: Luan, Nguyen Ngoc; Yen, Nguyen Dong
• Is Part Of: Optimization. Volume 69:Number 3(2020)
• Page Start: 471
• Page End: 492
• Publication Date: 2020-03-03
• Subjects: Convex polyhedron -- generalized convex polyhedron -- locally convex Hausdorff topological vector space -- representation formula -- generalized linear programming problem -- generalized linear vector optimization problem -- solution existence theorem; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1614179
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: It is well known that finite-dimensional polyhedral convex sets can be generated by finitely many points and finitely many directions. Representation formulas in this spirit are obtained for convex polyhedra and generalized convex polyhedra in locally convex Hausdorff topological vector spaces. Our results develop those of X. Y. Zheng (Set-Valued Anal. 2009;17:389–408), which were established in a Banach space setting. Applications of the representation formulas to proving solution existence theorems for generalized linear programming problems and generalized linear vector optimization problems are shown.