Linear complementarity problem
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In mathematics, the linear complementarity problem in linear algebra consists of starting with a known n-dimensional column vector q and a known n×n matrix M, and finding two n-dimensional vectors w and z such that:
- q = w − Mz
- wi ≥ 0 and zi ≥ 0 for each i
- wi×zi = 0 (i.e. either wi=0 or zi=0) for each i
There are several algorithms (e.g. Lemke's algorithm) dealing with specific cases of the linear complementarity problem. A linear complementarity problem has a unique solution if and only if M is a P-matrix.
[edit] See also
[edit] Further reading
- Cottle, Richard (1992). The linear complementarity problem. Boston, Mass. : Academic Press
