Skip to main content

Advertisement

SpringerLink
Log in

A Farkas-type theorem for interval linear inequalities

  • Short Communication
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

We describe a Farkas-type condition for strong solvability of interval linear inequalities. The result is used to derive several descriptions of the set of strong solutions and to show that this set forms a convex polytope.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Farkas, J.: Theorie der einfachen Ungleichungen. Journal für die Reine und Angewandte Mathematik 124, 1–27 (1902). doi:10.1515/crll.1902.124.1

  2. Fiedler, M., Nedoma, J., Ramík, J., Rohn, J., Zimmermann, K.: Linear Optimization Problems with Inexact Data. Springer, New York (2006)

    MATH  Google Scholar 

  3. Karademir, S., Prokopyev, O.A.: A short note on solvability of systems of interval linear equations. Linear Multilinear Algebra 59(6), 707–710 (2011). doi:10.1080/03081087.2010.486403

    Article  MATH  MathSciNet  Google Scholar 

  4. Rohn, J.: Linear programming with inexact data is NP-hard. Zeitschrift für Angewandte Mathematik und Mechanik 78(Supplement 3), S1051–S1052 (1998). doi:10.1002/zamm.19980781594

    Article  MATH  MathSciNet  Google Scholar 

  5. Rohn, J.: A residual existence theorem for linear equations. Optim. Lett. 4, 287–292 (2010). doi:10.1007/s11590-009-0160-7

    Article  MATH  MathSciNet  Google Scholar 

  6. Rohn, J.: Letter to the editor. Linear Multilinear Algebra 61, 697–698 (2013). doi:10.1080/03081087.2012.698617

    Article  MATH  MathSciNet  Google Scholar 

  7. Rohn, J., Kreslová, J.: Linear interval inequalities. Linear Multilinear Algebra 38, 79–82 (1994). doi:10.1080/03081089508818341

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The work was supported with institutional support RVO:67985807. The author wishes to thank an anonymous referee whose justified remarks on the earlier version of the manuscript resulted in essential reworking and enhancement of the paper.

Author information

Authors and Affiliations

  1. Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic

    Jiri Rohn

Authors
  1. Jiri Rohn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiri Rohn.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rohn, J. A Farkas-type theorem for interval linear inequalities. Optim Lett 8, 1591–1598 (2014). https://doi.org/10.1007/s11590-013-0675-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-013-0675-9

Keywords

Search

Navigation