## Abstract

In this note we consider the feasibility problem of oriented matroids. An alternative

theorem, which is a generalization of Farkas’ famous result, is stated and proved. Our proof is constructive and new. In the proof of the generalized Farkas lemma, the finiteness of a criss-cross type algorithm is used. The algorithm’s pivot rule, for criss-cross type methods, first was used by S. Zhang for linear programming problems.

theorem, which is a generalization of Farkas’ famous result, is stated and proved. Our proof is constructive and new. In the proof of the generalized Farkas lemma, the finiteness of a criss-cross type algorithm is used. The algorithm’s pivot rule, for criss-cross type methods, first was used by S. Zhang for linear programming problems.

Original language | English |
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Pages (from-to) | 423-431 |

Number of pages | 9 |

Journal | Pure Mathematics and Applications |

Volume | 13 |

Issue number | 4 |

Publication status | Published - 1 Dec 2002 |

## Keywords

- matroids
- oriented matroids
- feasibility problem of oriented matroids
- criss-cross type algorithm