Discrete convexity: Convexity for functions defined on discrete spaces
type: Item
instance of: scholarly article
title: Discrete convexity: Convexity for functions defined on discrete spaces
zbMATH Open document ID: 1025.26006
DOI: 10.1016/S0166-218X(01)00191-3
published in: Discrete Applied Mathematics
publication date: 2002-08-29T00:00:00Z
review text: The concept of discrete convexity for a real-valued function defined on a discrete space is an extension of the convexity definition of continuous functions. The equivalence of discrete convexity and the conventional definition of increasing (non-decreasing) first forward differences of functions of single variables is established. A further extension of the discrete convexity with submodularity yields the concept of strong discrete convexity. A strongly convex function is proved to have positive semidefinite matrix of second forward differences, and a partial converse of this result is provided.
reviewed by: Rita Pini
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 52A41
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 1792305
zbMATH Keywords: discrete convexity
zbMATH Keywords: strong discrete convexity
zbMATH Keywords: first and second forward differences
zbMATH Keywords: submodularity
author: Umit Yuceer
MaRDI profile type: Publication
cites work: Q5619190
cites work: Contraction Mappings in the Theory Underlying Dynamic Programming
cites work: Discrete Optimization Via Marginal Analysis
cites work: Discrete convex analysis
cites work: Marginal Allocation Algorithm For Nonseparable Functions
Wikidata QID: Q127532330
description: scientific article; zbMATH DE number 1792305