Discrete Fenchel duality for a pair of integrally convex and separable convex functions

Kazuo Murota, Akihisa Tamura

研究成果: Article査読

抄録

Discrete Fenchel duality is one of the central issues in discrete convex analysis. The Fenchel-type min–max theorem for a pair of integer-valued M-convex functions generalizes the min–max formulas for polymatroid intersection and valuated matroid intersection. In this paper we establish a Fenchel-type min–max formula for a pair of integer-valued integrally convex and separable convex functions. Integrally convex functions constitute a fundamental function class in discrete convex analysis, including both M-convex functions and L-convex functions, whereas separable convex functions are characterized as those functions which are both M-convex and L-convex. The theorem is proved by revealing a kind of box integrality of subgradients of an integer-valued integrally convex function. The proof is based on the Fourier–Motzkin elimination.

本文言語English
ページ(範囲)599-630
ページ数32
ジャーナルJapan Journal of Industrial and Applied Mathematics
39
2
DOI
出版ステータスPublished - 2022 5月

ASJC Scopus subject areas

  • 工学(全般)
  • 応用数学

フィンガープリント

「Discrete Fenchel duality for a pair of integrally convex and separable convex functions」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル