### Abstract

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 |

### Fingerprint

### Keywords

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

### Cite this

*Pure Mathematics and Applications*,

*13*(4), 423-431.

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*Pure Mathematics and Applications*, vol. 13, no. 4, pp. 423-431.

**A simple proof of the generalized farkas lemma for oriented matroids.** / Balogh, L.; Illes, T.; Erbilen, F.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A simple proof of the generalized farkas lemma for oriented matroids

AU - Balogh, L.

AU - Illes, T.

AU - Erbilen, F.

PY - 2002/12/1

Y1 - 2002/12/1

N2 - In this note we consider the feasibility problem of oriented matroids. An alternativetheorem, 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.

AB - In this note we consider the feasibility problem of oriented matroids. An alternativetheorem, 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.

KW - matroids

KW - oriented matroids

KW - feasibility problem of oriented matroids

KW - criss-cross type algorithm

M3 - Article

VL - 13

SP - 423

EP - 431

JO - Pure Mathematics and Applications

JF - Pure Mathematics and Applications

SN - 1218-4586

IS - 4

ER -