Scaling, proximity, and optimization of integrally convex functions

Satoko Moriguchi, Kazuo Murota, Akihisa Tamura, Fabio Tardella

研究成果: Article

7 引用 (Scopus)

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In discrete convex analysis, the scaling and proximity properties for the class of L(Formula presented.)-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 (Formula presented.), 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.

元の言語English
ページ(範囲)1-36
ページ数36
ジャーナルMathematical Programming
DOI
出版物ステータスAccepted/In press - 2018 1 24

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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