An experimental investigation of enumerative methods for the linear complementarity problem

The Linear Complementarity Problem (LCP) is that of finding vectors z ϵ R n and w ϵ R n such that w = q + Mz, z ⩾ 0, w ⩾ 0, z T w = 0, where qϵ R n and M is a n by n real matrix. This problem can be processed by enumerative tree-search methods, whose efficiency depends on a set of strategies to redu...

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Bibliographic Details
Published in:Computers & operations research 1988, Vol.15 (5), p.417-426
Main Authors: Júdice, J.J., Faustino, A.M.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Exact sciences and technology
Linear programming
Mathematical programming
Operational research and scientific management
Operational research. Management science
Operations research
Statistical analysis
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Summary:The Linear Complementarity Problem (LCP) is that of finding vectors z ϵ R n and w ϵ R n such that w = q + Mz, z ⩾ 0, w ⩾ 0, z T w = 0, where qϵ R n and M is a n by n real matrix. This problem can be processed by enumerative tree-search methods, whose efficiency depends on a set of strategies to reduce the search. In this paper a number of such strategies is discussed and an experimental investigation of the resulting enumerative methods on small and medium scale ( n ⩽ 500) sparse LCPs is presented. The applicability of these methods for general LCPs (without any assumption on the class of the matrix) and the numerical results presented in this paper show that it is worthwhile to use these methods for general medium scale sparse LCPs.
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/0305-0548(88)90058-5