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A homogeneous model for monotone mixed horizontal linear complementarity problems

Author

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  • Cosmin G. Petra

    (Lawrence Livermore National Laboratory)

  • Florian A. Potra

    (University of Maryland, Baltimore County)

Abstract

We propose a homogeneous model for the class of mixed horizontal linear complementarity problems. The proposed homogeneous model is always solvable and provides the solution of the original problem if it exists, or a certificate of infeasibility otherwise. Our formulation preserves the sparsity of the original formulation and does not reduce to the homogeneous model of the equivalent standard linear complementarity problem. We study the properties of the model and show that interior-point methods can be used efficiently for the numerical solutions of the homogeneous problem. Numerical experiments show convincingly that it is more efficient to use the proposed homogeneous model for the mixed horizontal linear complementarity problem than to use known homogeneous models for the equivalent standard linear complementarity problem.

Suggested Citation

  • Cosmin G. Petra & Florian A. Potra, 2019. "A homogeneous model for monotone mixed horizontal linear complementarity problems," Computational Optimization and Applications, Springer, vol. 72(1), pages 241-267, January.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:1:d:10.1007_s10589-018-0035-x
    DOI: 10.1007/s10589-018-0035-x
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    References listed on IDEAS

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    1. Gondzio, Jacek, 1995. "HOPDM (version 2.12) -- A fast LP solver based on a primal-dual interior point method," European Journal of Operational Research, Elsevier, vol. 85(1), pages 221-225, August.
    2. R. D. C. Monteiro & Jong-Shi Pang, 1996. "Properties of an Interior-Point Mapping for Mixed Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 629-654, August.
    3. R. D. C. Monteiro & Jong-Shi Pang, 1998. "On Two Interior-Point Mappings for Nonlinear Semidefinite Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 39-60, February.
    4. J. Frédéric Bonnans & Clovis C. Gonzaga, 1996. "Convergence of Interior Point Algorithms for the Monotone Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 1-25, February.
    5. Kuo-Ling Huang & Sanjay Mehrotra, 2017. "Solution of Monotone Complementarity and General Convex Programming Problems Using a Modified Potential Reduction Interior Point Method," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 36-53, February.
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