Relations Between PL Maps, Complementary Cones, and Degree in Linear Complementarity Problems

  • C. B. Garcia
  • F. J. Gould
  • T. R. Turnbull
Part of the NATO Conference Series book series (NATOCS, volume 13)


Let M be an n × n real matrix and q an n-vector. The problem
$${\text{find z }} \in {{\text{R}}^{\text{n}}}{\text{ and w}} \in {{\text{R}}^{\text{n}}}{\text{such that}}$$
(I, -M, q) w = q + Mz, w ≥ 0, z ≥ 0, and
$${{\rm{w}}^{\rm{T}}}{\rm{z = 0}}\left( {{\rm{i}}{\rm{.e}}{\rm{., }}{{\rm{w}}_{\rm{i}}}{\rm{ = 0 or }} {{\rm{z}}_{\rm{i}}}{\rm{ = 0 for i = l, }}...{\rm{, n}}} \right)$$
is called the linear complementarity problem (LCP). This problem is a canonical form for a variety of significant problems in mathematical progamming, economics and enginerring (e.g., references [2], [6], [9], [18–20], [24], [32]) and there is a wealth of literature on the problem (see, for example, references [3–5], [7], [10–17], [21–23], [25–28], [30–31], [33–43] and papers cited therein).


Complementarity Problem Linear Complementarity Problem North Pole Principal Minor Nondegenerate Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • C. B. Garcia
    • 1
  • F. J. Gould
    • 1
  • T. R. Turnbull
    • 1
  1. 1.Graduate School of BusinessUniversity of ChicagoUSA

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