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Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule

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  • S. R. Mohan

    (Delhi Centre)

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.

Suggested Citation

  • S. R. Mohan, 1997. "Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 409-423, August.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:2:d:10.1023_a:1022691830468
    DOI: 10.1023/A:1022691830468
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    References listed on IDEAS

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    1. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    2. B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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