### Abstract

The parametric linear complementarity problem is given by the conditions:q + αp + Mz ≥ 0, α ≥ 0, z ≥ 0, z^{T}(q + αp + Mz) = 0. Under the assumption that M is a P-matrix, Cottle proved that the solution map z(α) of the above problem is montonically nondecreasing in the parameter α for every nonnegative q and every p if and only if M is a Minkowski matrix. This paper examines whether a similar result holds in various other settings including a nonlinear case.

Original language | English |
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Pages (from-to) | 48-59 |

Number of pages | 12 |

Journal | Mathematical Programming |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1977 Dec 1 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

Kaneko, I. (1977). Isotone solutions of parametric linear complementarity problems.

*Mathematical Programming*,*12*(1), 48-59. https://doi.org/10.1007/BF01593768