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On the Parametric Linear Complementarity Problem

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  • R. A. Danao

Abstract

Consider the parametric linear complementarity problem w=Mz+q+λp, w≥0, z≥0, w T z=0, where p≠0, 0≠q≥0, and λ≥0. We show that a necessary condition for every complementary map z(λ) to be isotone for every nonzero q≥0 and every p is that M be either a P-matrix or a $$P_{{\text{ }}1}^* $$ -matrix. The Cottle necessary and sufficient conditions for strong and uniform isotonicity for P-matrices are restated, with slight modifications, for $$P_{{\text{ }}1}^* $$ -matrices.

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  • R. A. Danao, 1997. "On the Parametric Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 445-454, November.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:2:d:10.1023_a:1022699624785
    DOI: 10.1023/A:1022699624785
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    References listed on IDEAS

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    1. B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
    2. 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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    Cited by:

    1. Zukui Li & Marianthi Ierapetritou, 2010. "A method for solving the general parametric linear complementarity problem," Annals of Operations Research, Springer, vol. 181(1), pages 485-501, December.
    2. Adelgren, Nathan & Wiecek, Margaret M., 2016. "A two-phase algorithm for the multiparametric linear complementarity problem," European Journal of Operational Research, Elsevier, vol. 254(3), pages 715-738.

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