Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
rapid-communication

Reducibility bounds of objective functions over the integers

Published: 01 November 2023 Publication History

Abstract

We study the settings where we are given a separable objective function of n variables defined in a given box of integers. We show that in many cases we can replace the given objective function by a new function with a much smaller domain. Our results apply to linear functions as well as to nonlinear separable convex objective functions.

References

[1]
Alexander Barvinok, A Course in Convexity, vol. 54, American Mathematical Soc., 2002.
[2]
David Cox, John Little, Donal O'Shea, Moss Sweedler, Ideals, varieties, and algorithms, Am. Math. Mon. 101 (6) (1994) 582–586.
[3]
Jesus De Loera, Raymond Hemmecke, Matthias Köppe, Jon Lee, Shmuel Onn, Robert Weismantel, Report of focused research group: Nonlinear discrete optimization, Technical report Banff International Research Station for Mathematical Innovation and Discovery, July 2010, https://www.birs.ca/events/2010/focussed-research-groups/10frg140.
[4]
Eisenbrand, Friedrich; Hunkenschröder, Christoph; Klein, Kim-Manuel; Koutecký, Martin; Levin, Asaf; Onn, Shmuel (2019): An algorithmic theory of integer programming. https://arxiv.org/abs/1904.01361v3.
[5]
András Frank, Éva Tardos, An application of simultaneous Diophantine approximation in combinatorial optimization, Combinatorica 7 (1) (1987) 49–65.
[6]
Paul Gordan, Ueber die auflösung linearer gleichungen mit reellen coefficienten, Math. Ann. 6 (1) (1873) 23–28.
[7]
Hermann Minkowski, Geometrie der zahlen, (2 vol.) Teubner, Leipzig, 1910, (1896), 1896.

Index Terms

  1. Reducibility bounds of objective functions over the integers
      Index terms have been assigned to the content through auto-classification.

      Recommendations

      Comments

      Information & Contributors

      Information

      Published In

      cover image Operations Research Letters
      Operations Research Letters  Volume 51, Issue 6
      Nov 2023
      188 pages

      Publisher

      Elsevier Science Publishers B. V.

      Netherlands

      Publication History

      Published: 01 November 2023

      Author Tags

      1. Integer programming
      2. Analysis of algorithms
      3. Separable convex objective

      Qualifiers

      • Rapid-communication

      Contributors

      Other Metrics

      Bibliometrics & Citations

      Bibliometrics

      Article Metrics

      • 0
        Total Citations
      • 0
        Total Downloads
      • Downloads (Last 12 months)0
      • Downloads (Last 6 weeks)0
      Reflects downloads up to 13 Feb 2025

      Other Metrics

      Citations

      View Options

      View options

      Figures

      Tables

      Media

      Share

      Share

      Share this Publication link

      Share on social media