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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)

Abstract

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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References

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    Crapo, H. H., and G.-C. Rota, On the Foundations of Combinatorial Theory: Combinatorial Geometries ( Preliminary Edition ), The MIT Press, 1970.MATHGoogle Scholar
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    Eaves, B. C., and C. E. Lemke, “Equivalence of LCP and PLS”, Mathematics of Operations Research, Vol. 6, No. 4, November 1981.MathSciNetCrossRefGoogle Scholar
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    Eaves, B. C., and Herbert Scarf, “The Solution of Systems of Piecewise Linear Equations”, Mathematics of Operations Research, Vol. 1, No. 1, February 1976.MathSciNetMATHCrossRefGoogle Scholar
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    Zwart, Philip B., “Multivariate Splines with Nondegenerate Partitions”, SIAM Journal of Numerical Analysis, Vol. 10, No. 4, September 1973.MathSciNetCrossRefGoogle Scholar

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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