Skip to main content
Log in

On the generalized Wolf problem: Preprocessing of nonnegative large-scale linear programming problems with group constraints

  • Topical Issue
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Nonnegative large-scale linear programming problems with group constraints are extremely important for different applications in economics, technology, and other spheres. In this paper, we describe a new approach to preprocessing of these problems so that to reduce their dimensions considerably by defining and removing redundant constraints and variables.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ioslovich, I.V. and Makarenkov, Yu.M., On Methods for Dimension Reduction of Linear Programming Problems, Ekonom. Mat. Metody, 1975, vol. 11, no. 3, pp. 316–324.

    Google Scholar 

  2. Ioslovich, I., Robust Reduction of a Class of Large-Scale Linear Programs, SIAM J. Optim., 2001, vol. 12, no. 1, pp. 262–282.

    Article  MATH  Google Scholar 

  3. Dantzig, G.B., Linear Programming and Extensions, Princeton: Princeton Univ. Press, 1963.

    MATH  Google Scholar 

  4. Gill, Ph.E., Murray, W., and Wright, M.H., Numerical Linear Algebra and Optimization, Redwood City: Addison-Wesley, 1991.

    MATH  Google Scholar 

  5. Adler, I., Resende, G.C., Veiga, G., and Karmarkar, N., An Implementation of Karmarkar’s Algorithm for Linear Programming, Math. Program., Ser. A, 1989, vol. 44, no. 3, pp. 297–335.

    Article  MATH  Google Scholar 

  6. Bradley, G.H., Brown, G.G., and Graves, G.W., Structural Redundancy in Large-Scale Optimization Models, Karwan, M.H. et al., Eds., in Redundancy in Mathematical Programming, Heidelberg: Springer-Verlag, 1983, pp. 145–169.

    Google Scholar 

  7. Tomlin, J.A. and Welch, J.S., Formal Optimization of Some Reduced Linear Programming Problems, Math. Program., 1983, vol. 27, no. 2, pp. 232–240.

    Article  MATH  Google Scholar 

  8. Karwan, M.H., Lofti, F., Telgen, J., and Zionts, S., Redundancy in Mathematical Programming, Berlin: Springer-Verlag, 1983.

    MATH  Google Scholar 

  9. Fourer, R. and Gay, D.M., Experience with a Primal Presolve Algorithm, in Large Scale Optimization: State of the Art, Hager, W.W., Hearn, D.W., and Pardalos, P.M., Eds., Dordrecht: Academic, 1994, pp. 135–154.

    Google Scholar 

  10. Gould, N. and Toint, P.L., Preprocessing for Quadratic Programming, Math. Program., Ser. B, 2004, vol. 100, no. 1, pp. 95–132.

    MATH  Google Scholar 

  11. Cormen, T.H., Leiserson, R.L., and Rivest, R.L., Introduction to Algorithms, Cambridge: MIT Press, 2001.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © P.-O. Gutman, I. Ioslovich, 2007, published in Avtomatika i Telemekhanika, 2007, No. 8, pp. 116–125.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gutman, P.O., Ioslovich, I. On the generalized Wolf problem: Preprocessing of nonnegative large-scale linear programming problems with group constraints. Autom Remote Control 68, 1401–1409 (2007). https://doi.org/10.1134/S0005117907080115

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117907080115

PACS number

Navigation