Algorithms for the Generalized Linear Complementarity Problem with a Vertical Block Z -Matrix
S. R. Mohan, Sarmistha Neogy · SIAM Journal on Optimization · 1996
In this paper, we consider the generalized linear complementarily 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.