On Some Generalized Polyhedral Convex Constructions. (4th April 2018)
- Record Type:
- Journal Article
- Title:
- On Some Generalized Polyhedral Convex Constructions. (4th April 2018)
- Main Title:
- On Some Generalized Polyhedral Convex Constructions
- Authors:
- Luan, Nguyen Ngoc
Yao, Jen-Chih
Yen, Nguyen Dong - 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.
- Is Part Of:
- Numerical functional analysis and optimization. Volume 39:Number 5(2018)
- Journal:
- Numerical functional analysis and optimization
- Issue:
- Volume 39:Number 5(2018)
- Issue Display:
- Volume 39, Issue 5 (2018)
- Year:
- 2018
- Volume:
- 39
- Issue:
- 5
- Issue Sort Value:
- 2018-0039-0005-0000
- 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 - Journal URLs:
- http://www.tandfonline.com/toc/lnfa20/current ↗
http://www.tandfonline.com/ ↗ - DOI:
- 10.1080/01630563.2017.1387863 ↗
- Languages:
- English
- ISSNs:
- 0163-0563
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 6184.692000
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 5873.xml