Skip to main content
SpringerLink
Log in

Stability analysis in pure and mixed-integer linear programming

  • Integer Programming
  • Conference paper
  • First Online:
Optimization Techniques

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 23))

Abstract

We examine the stability behaviour of pure and mixed-integer linear programs for the case that the coefficients of the objective function and the right-hand sides of the constraints change their value. The stability of the program will be defined by using continuity properties of the extremal value, the constraints-set-mapping and the optimal set. The considerations are independent of compactness requirements imposed on the feasible set. It is, however, necessary to assume rationality of the constraints matrix.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • B.BANK, Qualitative Stabilitätsuntersuchungen rein-und gemischtganzzahliger linearer parametrischer Optimierungsprobleme Seminarbericht Nr. 6, Humboldt-Universität zu Berlin, 1978.

    Google Scholar 

  • B.BANK, J.GUDDAT, D.KLATTE, B.KUMMER, K.TAMMER, Nichtlineare parametrische Optimierung, Seminarbericht Nr., Humboldt-Universität zu Berlin, 1980 (to appear).

    Google Scholar 

  • C. BERGE, Espaces topologiques. Fonctions multivoques Dunod Paris, 1959.

    Google Scholar 

  • S. DOLECKI, Constraints stability and moduli of semicontinuiuy. 2nd IFAC Symp. on Distributed Parameter Systems, Warwick 1977 (Preprint)

    Google Scholar 

  • R.R. MEYER, Integer and mixed integer programming models: General properties, IOTA, Vol.16, (1975), No. 3/4

    Google Scholar 

  • H. NOLTEMEIER, Sensitivitätsanalyse bei diskreten linearen Optimierungsproblemen, Lecture Notes in Operations Research and Mathematical Systems No. 30, Springer Verlag, Berlin-Heidelberg-New York (1970)

    Google Scholar 

  • M. RADKE, Sensitivity Analysis in Discrete Optimization. Western Management Science Institute. University of California, Los Angeles, Working Paper 240, 1975

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sektion Mathematik, Humboldt-Universität zu BERLIN, Unter den Linden 6, 1086, Berlin, DDR

    B. Bank

Authors
  1. B. Bank
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

K. Iracki K. Malanowski S. Walukiewicz

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Bank, B. (1980). Stability analysis in pure and mixed-integer linear programming. In: Iracki, K., Malanowski, K., Walukiewicz, S. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006598

Download citation

  • DOI: https://doi.org/10.1007/BFb0006598

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10081-2

  • Online ISBN: 978-3-540-38253-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation