### Abstract

Linear Complementarity Problems (LCPs) belong to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Following our recently published ideas we generalize affine scaling and predictor-corrector interior point algorithms to solve LCPs with general matrices in EP-sense, namely, our generalized interior point algorithms either solve the problems with rational coefficient matrix in polynomial time or give a polynomial size certificate that our matrix does not belong to the set of P * (~κ) matrices, with arbitrary large, but apriori fixed, rational, positive ~κ.

Original language | English |
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Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Algorithmic Operations Research |

Volume | 5 |

Issue number | 1 |

Publication status | Published - 1 Jan 2010 |

### Keywords

- linear complementarity problem
- sufficient matrix
- interior point method
- affine scaling method
- predictor-corrector algorithm

## Cite this

Illes, T., Nagy, M., & Terlaky, T. (2010). Polynomial interior point algorithms for general linear complementarity problems.

*Algorithmic Operations Research*,*5*(1), 1-12.