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)

Abstract

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).

Keywords

Kelly Milton Tami 

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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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