Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets

Kazuo Murota; Akihisa Tamura

doi:10.1007/s13160-023-00635-1

Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets

Kazuo Murota, Akihisa Tamura

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, L^♮-convex sets, and M^♮-convex sets.

Original language	English
Pages (from-to)	987-1011
Number of pages	25
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	41
Issue number	2
DOIs	https://doi.org/10.1007/s13160-023-00635-1
Publication status	Published - 2024 May

Keywords

Characteristic cone
Discrete convex analysis
Integrally convex set
L-convex set
M-convex set
Minkowski sum

ASJC Scopus subject areas

General Engineering
Applied Mathematics

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10.1007/s13160-023-00635-1

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abstract = "Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, L♮-convex sets, and M♮-convex sets.",

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Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets

Abstract

Keywords

ASJC Scopus subject areas

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