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

被引：0

作者：

Murota, Kazuo ^{[1
,2
]}

Tamura, Akihisa ^{[3
]}

机构：

[1] Inst Stat Math, 10-3 Midori Cho, Tachikawa, Tokyo 1908562, Japan

[2] Tokyo Metropolitan Univ, Fac Econ & Business Adm, 1-1 Minami Osawa, Hachioji, Tokyo 1920397, Japan

[3] Keio Univ, Dept Math, 3-14-1 Hiyoshi,Kohoku Ku, Yokohama, Kanagawa 2238522, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2024年 / 41卷 / 02期

基金：

日本学术振兴会;

关键词：

Discrete convex analysis; Integrally convex set; L-(sic)-convex set; M-(sic)-convex set; Minkowski sum; Characteristic cone;

D O I：

10.1007/s13160-023-00635-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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-(sic)-convex sets, and M-(sic)-convex sets.

引用

页码：987 / 1011

页数：25

共 50 条

[1] Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets
Kazuo Murota
Akihisa Tamura
Japan Journal of Industrial and Applied Mathematics, 2024, 41 : 987 - 1011
[2] MINKOWSKI DECOMPOSITION OF CONVEX SETS
SALLEE, GT
ISRAEL JOURNAL OF MATHEMATICS, 1972, 12 (03) : 266 - &
[3] An outer approximation of the Minkowski sum of convex conic sets with application to demand response
Barot, Suhail
Taylor, Josh A.
2016 IEEE 55TH CONFERENCE ON DECISION AND CONTROL (CDC), 2016, : 4233 - 4238
[4] Shapley-Folkman-type theorem for integrally convex sets
Murota, Kazuo
Tamura, Akihisa
DISCRETE APPLIED MATHEMATICS, 2025, 360 : 42 - 50
[5] Recent progress on integrally convex functions
Murota, Kazuo
Tamura, Akihisa
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2023, 40 (03) : 1445 - 1499
[6] Recent progress on integrally convex functions
Kazuo Murota
Akihisa Tamura
Japan Journal of Industrial and Applied Mathematics, 2023, 40 : 1445 - 1499
[7] Scaling, proximity, and optimization of integrally convex functions
Moriguchi, Satoko
Murota, Kazuo
Tamura, Akihisa
Tardella, Fabio
MATHEMATICAL PROGRAMMING, 2019, 175 (1-2) : 119 - 154
[8] Integrality of subgradients and biconjugates of integrally convex functions
Murota, Kazuo
Tamura, Akihisa
OPTIMIZATION LETTERS, 2020, 14 (01) : 195 - 208
[9] Scaling, proximity, and optimization of integrally convex functions
Satoko Moriguchi
Kazuo Murota
Akihisa Tamura
Fabio Tardella
Mathematical Programming, 2019, 175 : 119 - 154
[10] Discrete Fenchel duality for a pair of integrally convex and separable convex functions
Murota, Kazuo
Tamura, Akihisa
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2022, 39 (02) : 599 - 630

← 1 2 3 4 5 →