On the convergence of the block principal pivotal algorithm for the LCP

On the convergence of the block principal pivotal algorithm for the LCP

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Article ID: iaor19991985
Country: Netherlands
Volume: 102
Issue: 3
Start Page Number: 657
End Page Number: 666
Publication Date: Nov 1997
Journal: European Journal of Operational Research
Authors: ,
Keywords: complementarity
Abstract:

We show that the block principal pivot algorithm (BPPA) for the linear complementarity problem (LCP) solves the problem for a special class of matrices in at most n block principal pivot steps. We provide cycling examples for the BPPA in which the matrix is positive definite or symmetric positive definite. For LCP of order three, we prove that strict column (row) diagonal dominance is a sufficient condition to avoid cycling.

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