The Dual Simplex Algorithm: Parametric Linear Programming

  • Michel Sakarovitch
Part of the Springer Texts in Electrical Engineering book series (STELE)

Abstract

Consider the pair of dual linear programs
$$(PC)\left\{ \begin{gathered}Ax \leqslant b\;x \geqslant 0 \hfill \\ cx = z(Max) \hfill \\\end{gathered} \right.\quad (DC)\left\{ \begin{gathered} yA \geqslant c\;y \geqslant 0 \hfill \\ yb = w(Min) \hfill \\ \end{gathered} \right.$$
written in canonical form. If b ≥ 0, then x = 0 is a feasible solution of (PC). We say in this case that (PC) is “primal feasible.” If c ≤ 0, then y = 0 is a feasible solution of (DC). In this case, we say that (PC) is “dual feasible.” Given a linear program written in canonical form with respect to a basis, we know (from Theorem IV.3) that this basis is optimal if and only if the linear program is at the same time primal and dual feasible.

Keywords

Lution Paral Cond Ques Tion Malit 

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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Michel Sakarovitch
    • 1
  1. 1.Laboratoire I.M.A.G.Université Scientifique et Medicale de GrenobleGrenoble CedexFrance

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