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A constructive characterization of \(Q_ 0\)-matrices with nonnegative principal minors. (English) Zbl 0618.90091

In a previous paper [ibid. 16, 374-377 (1979; Zbl 0416.90074)] we characterized the class of matrices with nonnegative principal minors for which the linear complementarity problem always has a solution. That class is contained in the one we study here. Our main result gives a finitely testable set of necessary and sufficient conditions under which a matrix with nonnegative principal minors has the property that if a corresponding linear complementarity problem is feasible then it is solvable. In short, we constructively characterize the matrix class known as \(Q_ 0\cap P_ 0\).

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Citations:

Zbl 0416.90074
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References:

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