Scaling, proximity, and optimization of integrally convex functions

Satoko Moriguchi, Kazuo Murota, Akihisa Tamura, Fabio Tardella

研究成果: Article査読

8 被引用数 (Scopus)

抄録

In discrete convex analysis, the scaling and proximity properties for the class of L -convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of integrally convex functions of n variables, we show here that the scaling property only holds when n≤ 2 , while a proximity theorem can be established for any n, but only with a superexponential bound. This is, however, sufficient to extend the classical logarithmic complexity result for minimizing a discrete convex function of one variable to the case of integrally convex functions of any fixed number of variables.

本文言語English
ページ(範囲)119-154
ページ数36
ジャーナルMathematical Programming
175
1-2
DOI
出版ステータスPublished - 2019 5 1

ASJC Scopus subject areas

  • ソフトウェア
  • 数学 (全般)

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