## Abstract

In this paper, we propose a generalized Newton method for solving a class of discrete-time linear complementarity systems consisting of a system of linear equations and a linear complementarity constraints with a Z-matrix. We obtain a complete characterization of the least element solution of a linear complementarity problem with a Z-matrix that a solution is the least element solution if and only if the principal submatrix corresponding to the nonzero components of the solution is an M-matrix. We present a Newton method for solving a linear complementarity problem with a Z-matrix. We propose a generalized Newton method for solving the discrete-time linear complementarity system where the linear complementarity problem constraint is solved by the proposed Newton method. Under suitable conditions, we show that the generalized Newton method converges globally and finds a solution in finitely many iterations. Preliminary numerical results show the efficiency of the proposed method.

Original language | English |
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Pages (from-to) | 39-48 |

Number of pages | 10 |

Journal | European Journal of Operational Research |

Volume | 286 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Oct 2020 |

## Keywords

- Finite termination
- Generalized Newton method
- Least element solution
- Linear complementarity system
- Linear rate of convergence
- Z-matrix

## ASJC Scopus subject areas

- General Computer Science
- Modelling and Simulation
- Management Science and Operations Research
- Information Systems and Management