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A generalized Newton method for a class of discrete-time linear complementarity systems

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  • Sun, Zhe
  • Yang, Xiaoqi

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.

Suggested Citation

  • Sun, Zhe & Yang, Xiaoqi, 2020. "A generalized Newton method for a class of discrete-time linear complementarity systems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 39-48.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:1:p:39-48
    DOI: 10.1016/j.ejor.2020.03.058
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    References listed on IDEAS

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    1. Polyak, B.T., 2007. "Newton's method and its use in optimization," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1086-1096, September.
    2. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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