Proximity theorems of discrete convex functions

Kazuo Murota, Akihisa Tamura

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume99
Issue number3
DOIs
Publication statusPublished - 2004 Apr
Externally publishedYes

Fingerprint

Proximity
Convex function
Theorem
Polymatroid
Resource Allocation
Resource allocation
Efficient Algorithms
Optimal Solution
Intersection
Optimization Problem
Optimization problem
Reviewing
Allocation problem
Optimal solution

Keywords

  • Discrete convex analysis
  • Optimality criteria
  • Proximity properties

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)
  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research
  • Software
  • Computer Graphics and Computer-Aided Design
  • Computer Science(all)

Cite this

Proximity theorems of discrete convex functions. / Murota, Kazuo; Tamura, Akihisa.

In: Mathematical Programming, Vol. 99, No. 3, 04.2004, p. 539-562.

Research output: Contribution to journalArticle

Murota, Kazuo ; Tamura, Akihisa. / Proximity theorems of discrete convex functions. In: Mathematical Programming. 2004 ; Vol. 99, No. 3. pp. 539-562.
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