Advertisement

On a class of iterative projection and contraction methods for linear programming

  • B. S. He
Contributed Papers

Abstract

In this paper, based on the idea of a projection and contraction method for a class of linear complementarity problems (Refs. 1 and 2), we develop a class of iterative algorithms for linear programming with linear speed of convergence. The algorithms are used to solve transportation and network problems with up to 10,000 variables. Our experiments indicate that the algorithms are simple, easy to parallelize, and more efficient for some large practical problems.

Key Words

Projection methods Fejér contraction linear complementarity problems linear programming network programming 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    He, B.,A Saddle-Point Algorithm for Linear Programming, Nanjing Daxue Xuebao, Shuxue Banniankan, Vol. 6, pp. 41–48, 1989.Google Scholar
  2. 2.
    He, B.,A Projection and Contraction Method for a Class of Linear Complementarity Problems and Its Application in Convex Quadratic Programming, Applied Mathematics and Optimization, Vol. 25, pp. 247–262, 1992.Google Scholar
  3. 3.
    Mangasarian, O. L.,Solution of Symmetric Linear Complementarity Problems by Iterative Methods, Journal of Optimization Theory and Applications, Vol. 22, pp. 465–485, 1979.Google Scholar
  4. 4.
    Dantzig, G. B.,Linear Programming and Extensions, Princeton University Press, Princeton, New Jersey, 1963.Google Scholar
  5. 5.
    Blum, E., andOettli, W.,Mathematische Optimierung, Springer-Verlag, Berlin, Germany, 1975.Google Scholar
  6. 6.
    Uzawa, H.,Iterative Methods for Concave Programming, Studies in Linear and Nonlinear Programming, Edited by K. J. Arrow et. al., Stanford University Press, Stanford, California, pp. 154–165, 1958.Google Scholar
  7. 7.
    He, B., andStoer, J.,Solution of Projection Problems over Polytopes, Numerische Mathematik, Vol. 61, pp. 73–90, 1992.Google Scholar
  8. 8.
    Korpelevich, G. M.,The Extragradient Method for Finding Saddle Points and Other Problems, Ekonomika i Matematicheskie Metody, Vol. 22, pp. 747–756, 1976.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • B. S. He
    • 1
  1. 1.Department of MathematicsUniversity of NanjingNanjingChina

Personalised recommendations