Academic Journal
View in EDS

On the number of degenerate simplex pivots.

Bibliographic Details
Title: On the number of degenerate simplex pivots.
Authors: Kukharenko, Kirill1 (AUTHOR) kirill.kukharenko@ovgu.de, Sanità, Laura2 (AUTHOR) laura.sanita@unibocconi.it
Source: Mathematical Programming. Mar2026, Vol. 216 Issue 1/2, p757-791. 35p.
Subject Terms: *Linear programming, Simplex algorithm, Polyhedra, Iterative methods (Mathematics)
Abstract: The simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to move to a better extreme point along an improving edge-direction of the underlying polyhedron. A key issue in the simplex algorithm's performance is degeneracy, which may lead to a (potentially long) sequence of basis exchanges which do not change the current extreme point solution. In this paper, we prove that one can employ any improving feasible direction at an extreme point to limit the number of consecutive degenerate pivots that the simplex algorithm performs to n - m - 1 , where n is the number of variables and m is the number of equality constraints of a given LP in standard equality form. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Programming is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Business Source Index
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://dx.doi.org/doi:10.1007/s10107-026-02349-x
    Name: EDS - Springer Nature Journals (s7799221)
    Category: fullText
    Text: View record at Springer
  – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:bsx&genre=article&issn=00255610&ISBN=&volume=216&issue=1%2F2&date=20260301&spage=757&pages=757-791&title=Mathematical Programming&atitle=On%20the%20number%20of%20degenerate%20simplex%20pivots.&aulast=Kukharenko%2C%20Kirill&id=DOI:10.1007/s10107-026-02349-x
    Name: Full Text Finder (for New FTF UI) (ns324271)
    Category: fullText
    Text: Full Text Finder
    MouseOverText: Full Text Finder
Header DbId: bsx
DbLabel: Business Source Index
An: 193308462
RelevancyScore: 1390
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 1390.35424804688
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: On the number of degenerate simplex pivots.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Kukharenko%2C+Kirill%22">Kukharenko, Kirill</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kirill.kukharenko@ovgu.de</i><br /><searchLink fieldCode="AR" term="%22Sanità%2C+Laura%22">Sanità, Laura</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> laura.sanita@unibocconi.it</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Mathematical+Programming%22">Mathematical Programming</searchLink>. Mar2026, Vol. 216 Issue 1/2, p757-791. 35p.
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: *<searchLink fieldCode="DE" term="%22Linear+programming%22">Linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Simplex+algorithm%22">Simplex algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22Polyhedra%22">Polyhedra</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to move to a better extreme point along an improving edge-direction of the underlying polyhedron. A key issue in the simplex algorithm's performance is degeneracy, which may lead to a (potentially long) sequence of basis exchanges which do not change the current extreme point solution. In this paper, we prove that one can employ any improving feasible direction at an extreme point to limit the number of consecutive degenerate pivots that the simplex algorithm performs to n - m - 1 , where n is the number of variables and m is the number of equality constraints of a given LP in standard equality form. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Mathematical Programming is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=bsx&AN=193308462
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s10107-026-02349-x
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 35
        StartPage: 757
    Subjects:
      – SubjectFull: Linear programming
        Type: general
      – SubjectFull: Simplex algorithm
        Type: general
      – SubjectFull: Polyhedra
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
    Titles:
      – TitleFull: On the number of degenerate simplex pivots.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Kukharenko, Kirill
      – PersonEntity:
          Name:
            NameFull: Sanità, Laura
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 00255610
          Numbering:
            – Type: volume
              Value: 216
            – Type: issue
              Value: 1/2
          Titles:
            – TitleFull: Mathematical Programming
              Type: main
ResultId 1