An extension of Lemke’s method for the solution of a generalized Linear Complementarity Problem

  • Joaquim J. Júdice
  • J. Machado
  • Ana M. Faustino
II Mathematical Programming II.3 Linear Programming And Complementarity
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)


In this paper an extension of Lemke’s method for the solution of the Linear Complementarity Problem with Bounds (BLCP) is presented. This problem consists of finding vectors z∈Rn and w∈Rn such that
$$\begin{gathered}w = q + Mz \hfill \\a_i \leqslant z_i \leqslant b_i \hfill \\z_i = a_i \Rightarrow w_i \geqslant 0 i = 1,...,n \hfill \\z_i = b_i \Rightarrow w_i \leqslant 0 \hfill \\a_i < z_i < b_i \Rightarrow w_i = 0 \hfill \\\end{gathered}$$
where q∈Rn and M∈Rn×n are given and −∞≤ai<bi≤+∞ for all i=1,..., n. It is shown that the algorithm can process the BLCP when M is a positive semi-definite matrix or when all the bounds ai and bi are finite. The performance of the algorithm for the solution of large-scale BLCPs is briefly discussed.


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Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Joaquim J. Júdice
    • 1
  • J. Machado
    • 1
  • Ana M. Faustino
    • 2
  1. 1.Departamento de MatemáticaUniversidade de CoimbraCoimbraPortugal
  2. 2.Departamento de Engenharia CivilUniversidade de PortoPortoPortugal

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