Homotopy Methods and Global Convergence pp 91-144 | Cite as

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

Chapter

## Abstract

Let M be an n × n real matrix and q an n-vector. The problem
(I, -M, q) w = q + Mz, w ≥ 0, z ≥ 0, and
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).

$${\text{find z }} \in {{\text{R}}^{\text{n}}}{\text{ and w}} \in {{\text{R}}^{\text{n}}}{\text{such that}}$$

$${{\rm{w}}^{\rm{T}}}{\rm{z = 0}}\left( {{\rm{i}}{\rm{.e}}{\rm{., }}{{\rm{w}}_{\rm{i}}}{\rm{ = 0 or }}
{{\rm{z}}_{\rm{i}}}{\rm{ = 0 for i = l, }}...{\rm{, n}}} \right)$$

## Keywords

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