On the Equivalence of the Linear Complementarity Problem and a System of Piecewise Linear Equations: Part II

  • B. C. Eaves
  • C. E. Lemke
Part of the NATO Conference Series book series (NATOCS, volume 13)


In an earlier paper the authors demonstrated the equivalence of the linear complementarity problem and that of finding the zeroes of a square system of equations for which the functions are piecewise linear. Given the system of equations, a “dual” concept of complementarity was evoked to pose the problem as an LCP.

In this paper, with the simplifying assumption of a non-degenerate finite sub-division defined by hyperplanes, a simplified equivalence is demonstrated, wherein “complementarity” refers only to the positive vs negative sides of a hyperplane.

Key words

Piecewise linear linear complementarity subdivision by hyperplanes Non-degenerate 


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Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • B. C. Eaves
    • 1
  • C. E. Lemke
    • 2
  1. 1.Department of Operations ResearchStanford UniversityStanfordUSA
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

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