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Algorithms for the generalized linear complementarity problem with a vertical block \(Z\)-matrix. (English) Zbl 0868.90125

Summary: We consider the generalized linear complementarity problem VLCP \((q,A)\) where \(A\) is a vertical block \(Z\)-matrix. We prove that the Cottle-Dantzig pivoting algorithm can process this problem by showing that this algorithm generates the same sequence of bases that a modified simplex algorithm for minimizing the artificial variable \(z_0\) does. We also show that a modified version of the Cottle-Dantzig algorithm can be used for determining whether a given vertical block \(Z\)-matrix is a vertical block \(P_0\)-matrix.

MSC:

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