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Solution of linear complementarity problems by linear programming

Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 506)

Abstract

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

Mz+q≧0, z≧0, zT (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 Rn.

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© Springer-Verlag 1976

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