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Sufficient matrices and the linear complementarity problem. (English) Zbl 0674.90092
A new class of matrices, related to the linear complementarity problem (LCP), the so called “row sufficient” matrices, are introduced. Respectively, the transpose of such a matrix is called “column sufficient”. Two important results are proved: (i) A matrix $M$ is row sufficient iff for every $q\in \Bbb R^n$ any Kuhn-Tucker-point of the associated quadratic program solves the LCP $(q,M)$; (ii) $M$ is column sufficient iff for every $q\in \Bbb R^n$ the LCP $(q,M)$ has a convex solution set. The connections with other well-known matrix classes in linear complementarity theory are also discussed.
Reviewer: E.Iwanow

90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
15B57Hermitian, skew-Hermitian, and related matrices
Full Text: DOI
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