Computational Optimization and Applications

, Volume 72, Issue 1, pp 241–267 | Cite as

A homogeneous model for monotone mixed horizontal linear complementarity problems

  • Cosmin G. PetraEmail author
  • Florian A. Potra


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.


Mixed horizontal LCP Homogenization Interior-point method 



The work of Cosmin Petra was done the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The work of Florian Potra was supported by the National Science Foundation under Grant No. DMS-1311923.


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Authors and Affiliations

  1. 1.Center for Applied Scientific ComputingLawrence Livermore National LaboratoryLivermoreUSA
  2. 2.Department of Mathematics and StatisticsUniversity of Maryland, Baltimore CountyBaltimoreUSA

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