Scaling, proximity, and optimization of integrally convex functions

Satoko Moriguchi, Kazuo Murota, Akihisa Tamura, Fabio Tardella

Research output: Contribution to journalArticle

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalMathematical Programming
Publication statusAccepted/In press - 2018 Jan 24

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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