Convex Analysis and Duality over Discrete Domains

The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain. By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains, we study duals of optimization problems whose decision pa...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the Operations Research Society of China (Internet) 2018-06, Vol.6 (2), p.189-247
Main Authors: Adıvar, Murat, Fang, Shu-Cherng
Format: Article
Language:English
Subjects:
Convex analysis
Convexity
Decision theory
Domains
Integer programming
Linear programming
Mathematical functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain. By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains, we study duals of optimization problems whose decision parameters are integers. In particular, we construct duality theory for integer linear programming, provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.
ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-017-0158-2