Abstract
In this paper, we use the theory of degeneracy graphs recently developed by Gal et al. to introduce a graph for studying the adjacency of almost complementary feasible bases, some of which may be degenerate, which are of interest in the context of the linear complementarity problem. We study the structure of this graph with particular reference to the possibility of cycling and various anticycling rules in the Lemke complementary pivoting algorithm. We consider the transition node pivot rule introduced by Geue and show that this rule helps in avoiding cycling in the Lemke complementary pivoting algorithm under a suitable assumption.
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Mohan, S.R. Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule. Journal of Optimization Theory and Applications 94, 409–423 (1997). https://doi.org/10.1023/A:1022691830468
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DOI: https://doi.org/10.1023/A:1022691830468