Skip to main content
SpringerLink
Log in

Correction of improper linear programming problems in canonical form by applying the minimax criterion

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Given an inconsistent system of linear algebraic equations, necessary and sufficient conditions are established for the solvability of the problem of its matrix correction by applying the minimax criterion with the assumption that the solution is nonnegative. The form of the solution to the corrected system is presented. Two formulations of the problem are considered, specifically, the correction of both sides of the original system and correction with the right-hand-side vector being fixed. The minimax-criterion correction of an improper linear programming problem is reduced to a linear programming problem, which is solved numerically in MATLAB.

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

Similar content being viewed by others

References

  1. A. A. Vatolin, “Approximation of Improper Linear Programming Problems Using Euclidean Norm Criterion,” Comput. Math. Math. Phys. 24, 1907–1908 (1984).

    MathSciNet  MATH  Google Scholar 

  2. V. A. Gorelik, “Matrix Correction of a Linear Programming Problem with Inconsistent Constraints,” Comput. Math. Math. Phys. 41, 1615–1622 (2001).

    MathSciNet  MATH  Google Scholar 

  3. V. A. Gorelik, V. I. Erokhin, and R. V. Pechenkin, Numerical Methods for Correction of Improper Linear Programming Problems and Structural Systems of Equations (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2006) [in Russian].

    Google Scholar 

  4. R. R. Ibatullin, Candidate’s Dissertation in Mathematics and Physics (Moscow, 2002).

  5. V. V. Voevodin and Yu. A. Kuznetsov, Matrices and Computations (Nauka, Moscow, 1984) [in Russian].

Download references

Author information

Authors and Affiliations

  1. Moscow Pedagogical State University, Malaya Pirogovskaya ul. 1, Moscow, 119991, Russia

    O. S. Barkalova

Authors
  1. O. S. Barkalova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. S. Barkalova.

Additional information

Original Russian Text © O.S. Barkalova, 2012, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2012, Vol. 52, No. 12, pp. 2178–2189.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barkalova, O.S. Correction of improper linear programming problems in canonical form by applying the minimax criterion. Comput. Math. and Math. Phys. 52, 1624–1634 (2012). https://doi.org/10.1134/S0965542512120044

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542512120044

Keywords

Search

Navigation