The FARKAS Lemma

  • Achim Bachem
  • Walter Kern
Part of the Universitext book series (UTX)


The result mentioned at the end of Section 3.2, which relates the emptiness of a given polyhedron to the nonemptiness of a certain other polyhedron is wellknown as the FARKAS Lemma. We will state this theorem in a more precise form in this section. Moreover, we shall give several equivalent formulations of the FARKAS Lemma, which we derive from each other by introducing standard techniques in polyhedral theory. In particular, we will show that the FARKAS Lemma can be seen as a theorem relating a subspace L of Kn to its orthogonal complement L in the sense of Theorem 2.10.


Half Space Linear Subspace Orthogonal Complement Polyhedral Cone Close Half Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Achim Bachem
    • 1
  • Walter Kern
    • 2
  1. 1.Mathematisches InstitutUniversität zu KölnKöln 41Fed. Rep. of Germany
  2. 2.Department of Applied MathematicsUniversity of TwenteAE EnschedeThe Netherlands

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