## Abstract

In this paper, we reformulate the extended vertical linear complementarity problem (EVLCP(m, q)) as a nonsmooth equation H(t, x) = 0, where H : ℝ^{n+l} → ℝ^{n+1}, t ∈ ℝ is a parameter variable, and cursive Greek chi ∈ ℝ is the original variable. H is continuously differeritiable except at such points (t, cursive Greek chi) with t = 0. Furthermore H is strongly semismooth. The reformulation of EVLCP(m, q) as a nonsmooth equation is based on the so-called aggregation (smoothing) function. As a result, a Newton-type method is proposed which generates a sequence {w^{k} = (t^{k},cursive Greek chi^{k})} with all t^{k} > 0. We prove that every accumulation point of this sequence is a solution of EVLCP(M, q) under the assumption of row W_{0}-property. If row W-property holds at the solution point, then the convergence rate is quadratic. Promising numerical results are also presented.

Original language | English |
---|---|

Pages (from-to) | 45-66 |

Number of pages | 22 |

Journal | SIAM Journal on Matrix Analysis and Applications |

Volume | 21 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1999 |

## Scopus Subject Areas

- Analysis

## User-Defined Keywords

- Aggregation function
- Global convergence
- Semismoothness
- Smoothing Newton method