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Zbl 0674.90092
Cottle, R.W.; Pang, J.-S.; Venkateswaran, V.
Sufficient matrices and the linear complementarity problem.
(English)
[J] Linear Algebra Appl. 114-115, 231-249 (1989). ISSN 0024-3795

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. \par The connections with other well-known matrix classes in linear complementarity theory are also discussed.
[E.Iwanow]
MSC 2000:
*90C33 Complementarity problems
15A57 Other types of matrices

Keywords: row sufficient matrices; linear complementarity problem; column sufficient

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