Proximity theorems of discrete convex functions

Kazuo Murota, Akihisa Tamura

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


A proximity theorem is a statement that, given an optimization problem and its relaxation, an optimal solution to the original problem exists in a certain neighborhood of a solution to the relaxation. Proximity theorems have been used successfully, for example, in designing efficient algorithms for discrete resource allocation problems. After reviewing the recent results for L-convex and M-convex functions, this paper establishes proximity theorems for larger classes of discrete convex functions, L2-convex functions and M 2-convex functions, that are relevant to the polymatroid intersection problem and the submodular flow problem.

Original languageEnglish
Pages (from-to)539-562
Number of pages24
JournalMathematical Programming
Issue number3
Publication statusPublished - 2004 Apr
Externally publishedYes


  • Discrete convex analysis
  • Optimality criteria
  • Proximity properties

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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