Numerical Analysis pp 166-175 | Cite as

# Solution of linear complementarity problems by linear programming

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## Abstract

The linear complementarity problem is that of finding an n x 1 vector z such that

Mz+q≧0, z≧0, z^{T} (Mz+q)=0 where M is a given n x n real matrix and q is a given n x 1 vector. In this paper the class of matrices M for which this problem is solvable by a single linear program is enlarged to include matrices other than those that are z-matrices or those that have an inverse which is a z-matrix. (A Z-matrix is real square matrix with nonpositive offdiagonal elements.) Included in this class are other matrices such as nonnegative matrices with a strictly dominant diagonal and matrices that are the sum of a Z-matrix having a nonnegative inverse and the tensor product of any two positive vectors in R^{n}.

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