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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 n any Kuhn-Tucker-point of the associated quadratic program solves the LCP (q,M); (ii) M is column sufficient iff for every q 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

MSC:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
15A57Other types of matrices (MSC2000)