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The Simplex Method

In: Linear and Nonlinear Programming

Author

Listed:
  • David G. Luenberger

    (Stanford University)

  • Yinyu Ye

    (Stanford University)

Abstract

The idea of the simplex method is to proceed from one basic feasible solution (that is, one extreme point) of the constraint set of a problem in standard form to another, in such a way as to continually decrease the value of the objective function until a minimum is reached. The results of Chap. 2 assure us that it is sufficient to consider only basic feasible solutions in our search for an optimal feasible solution. This chapter demonstrates that an efficient method for moving among basic solutions to the minimum can be constructed.

Suggested Citation

  • David G. Luenberger & Yinyu Ye, 2016. "The Simplex Method," International Series in Operations Research & Management Science, in: Linear and Nonlinear Programming, edition 4, chapter 0, pages 33-82, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-18842-3_3
    DOI: 10.1007/978-3-319-18842-3_3
    as

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