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A method for solving the general parametric linear complementarity problem

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  • Zukui Li
  • Marianthi Ierapetritou

Abstract

This paper presents a solution method for the general (mixed integer) parametric linear complementarity problem pLCP(q(θ),M), where the matrix M has a general structure and integrality restriction can be enforced on the solution. Based on the equivalence between the linear complementarity problem and mixed integer feasibility problem, we propose a mixed integer programming formulation with an objective of finding the minimum 1-norm solution for the original linear complementarity problem. The parametric linear complementarity problem is then formulated as multiparametric mixed integer programming problem, which is solved using a multiparametric programming algorithm. The proposed method is illustrated through a number of examples. Copyright Springer Science+Business Media, LLC 2010

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  • 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.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:485-501:10.1007/s10479-010-0770-6
    DOI: 10.1007/s10479-010-0770-6
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    References listed on IDEAS

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    1. R. A. Danao, 1997. "On the Parametric Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 445-454, November.
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    3. R. Chandrasekaran & S. N. Kabadi & R. Sridhar, 1998. "Integer Solution for Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 390-402, May.
    4. Gailly, B. & Installe, M. & Smeers, Y., 2001. "A new resolution method for the parametric linear complementarity problem," European Journal of Operational Research, Elsevier, vol. 128(3), pages 639-646, February.
    5. GAILLY, Benoît & INSTALLE, Michel & SMEERS, Yves, 2001. "A new resolution method for the parametric linear complementarity problem," LIDAM Reprints CORE 1491, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Eaves, B. Curtis, 1976. "A finite algorithm for the linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 197-203, July.
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    Cited by:

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    2. Leilei Zhang & Guping Hu & Lizhi Wang & Yihsu Chen, 2016. "A bottom-up biofuel market equilibrium model for policy analysis," Annals of Operations Research, Springer, vol. 236(1), pages 75-101, January.
    3. 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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