On Some Generalized Polyhedral Convex Constructions. (4th April 2018)

• Record Type: Journal Article
• Authors: Luan, Nguyen Ngoc; Yao, Jen-Chih; Yen, Nguyen Dong
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 5(2018)
• Page Start: 537
• Page End: 570
• Publication Date: 2018-04-04
• Subjects: Conjugate function -- face -- finite representation -- generalized polyhedral convex function -- generalized polyhedral convex set -- infimal convolution -- separation theorem; 46A22 -- 49J27 -- 49N15 -- 90C25 -- 90C46; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1387863
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Generalized polyhedral convex sets, generalized polyhedral convex functions on locally convex Hausdorff topological vector spaces, and the related constructions such as sum of sets, sum of functions, directional derivative, infimal convolution, normal cone, conjugate function, subdifferential are studied thoroughly in this paper. Among other things, we show how a generalized polyhedral convex set can be characterized through the finiteness of the number of its faces. In addition, it is proved that the infimal convolution of a generalized polyhedral convex function and a polyhedral convex function is a polyhedral convex function. The obtained results can be applied to scalar optimization problems described by generalized polyhedral convex sets and generalized polyhedral convex functions.