Mohan, S. R.; Neogy, S. K. Algorithms for the generalized linear complementarity problem with a vertical block \(Z\)-matrix. (English) Zbl 0868.90125 SIAM J. Optim. 6, No. 4, 994-1006 (1996). 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. Cited in 5 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) Keywords:almost proper basis matrix; secondary proper ray; generalized linear complementarity; modified simplex algorithm; vertical block \(Z\)-matrix PDFBibTeX XMLCite \textit{S. R. Mohan} and \textit{S. K. Neogy}, SIAM J. Optim. 6, No. 4, 994--1006 (1996; Zbl 0868.90125) Full Text: DOI