### Abstract

Language | English |
---|---|

Pages | 233-238 |

Number of pages | 5 |

Journal | Journal of Optimization Theory and Applications |

Volume | 140 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- linear complementarity problem
- dual LCP
- row sufficient matrix
- ℘*-matrix
- EP theorem

### Cite this

*Journal of Optimization Theory and Applications*,

*140*(2), 233-238. https://doi.org/10.1007/s10957-008-9440-0

}

*Journal of Optimization Theory and Applications*, vol. 140, no. 2, pp. 233-238. https://doi.org/10.1007/s10957-008-9440-0

**EP theorem for dual linear complementarity problem.** / Illes, T.; Nagy, M.; Terlaky, T.

Research output: Contribution to journal › Article

TY - JOUR

T1 - EP theorem for dual linear complementarity problem

AU - Illes, T.

AU - Nagy, M.

AU - Terlaky, T.

PY - 2009

Y1 - 2009

N2 - The linear complementarity problem (LCP) belongs to the class of -hard problems. Therefore, we cannot expect a polynomial time solution method for LCPs without requiring some special property of the matrix of the problem. We show that the dual LCP can be solved in polynomial time if the matrix is row sufficient; moreover, in this case, all feasible solutions are complementary. Furthermore, we present an existentially polytime (EP) theorem for the dual LCP with arbitrary matrix.

AB - The linear complementarity problem (LCP) belongs to the class of -hard problems. Therefore, we cannot expect a polynomial time solution method for LCPs without requiring some special property of the matrix of the problem. We show that the dual LCP can be solved in polynomial time if the matrix is row sufficient; moreover, in this case, all feasible solutions are complementary. Furthermore, we present an existentially polytime (EP) theorem for the dual LCP with arbitrary matrix.

KW - linear complementarity problem

KW - dual LCP

KW - row sufficient matrix

KW - ℘-matrix

KW - EP theorem

UR - http://dx.doi.org/10.1007/s10957-008-9440-0

U2 - 10.1007/s10957-008-9440-0

DO - 10.1007/s10957-008-9440-0

M3 - Article

VL - 140

SP - 233

EP - 238

JO - Journal of Optimization Theory and Applications

T2 - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 2

ER -