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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. 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.
    2. 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).
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    4. R. A. Danao, 1997. "On the Parametric Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 445-454, November.
    5. Vivek Dua & Efstratios Pistikopoulos, 2000. "An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems," Annals of Operations Research, Springer, vol. 99(1), pages 123-139, December.
    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. 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.
    3. 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.

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