Advertisement

Linear Programming

  • D. Lloyd Smith
Part of the International Centre for Mechanical Sciences book series (CISM, volume 299)

Abstract

Linear programming is the branch of optimisation which is probably most often used in connection with problems of structural engineering — in the generic modelling of some types of problem or in the approximation of other more complicated ones. A review is made of the Simplex algorithm for linear programming in its two-phase form, and the program solution is related to the Karush-Kuhn-Tucker optimality conditions. The duality of linear programming is described in terms of the associated Lagrangian, and the optimal solution of the dual linear program is obtained from the Simplex solution of the primal problem through the Simplex multipliers.

Keywords

Basic Variable Linear Complementarity Problem Simplex Algorithm Artificial Variable Basic Feasible Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dantzig, G. B., Linear Programming and Extensions, Princeton 1963.Google Scholar
  2. 2.
    Gass, S. I., Linear Programming, Methods and Applications (3rd Ed.) McGraw-Hill 1969.Google Scholar
  3. 3.
    Hadley, G., Linear Programming, Addison-Wesley 1962.Google Scholar
  4. 4.
    Orchard-Hays, W., Advanced Linear Programming Computing Techniques, McGraw-Hill 1968.Google Scholar
  5. 5.
    Karmarkar, N., A new polynomial-time algorithm for linear programming, Combinatorica, 4 (1984) 373–396.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Murty, K. G., Complementarity problems, in: Mathematical Programming for Operational Researchers and Computer Scientists (Ed. A. G. Holzman ), Dekker 1981, 173–196.Google Scholar
  7. 7.
    Lemke, C. E., Recent results on complementarity problems, in: Nonlinear Programming (Eds. J. B. Rosen, O. L. Mangasarian and K. Ritter ), Academic Press 1970, 349–384.Google Scholar
  8. 8.
    Lemke, C. E., A survey of complementarity theory, in: Variational Inequalities and Complementarity Problems (Eds, R. W. Cottle, F. Giannessi and J-L. Lions ), Wiley 1980, 213–239.Google Scholar
  9. 9.
    Gale, D., Kuhn, H. W. and Tucker, A. W., Linear programming and the theory of games, in: Activity Analysis of Production and Allocation (Ed. T. C. Koopmans ), Wiley 1951.Google Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

  • D. Lloyd Smith
    • 1
  1. 1.Imperial CollegeLondonUK

Personalised recommendations