Annals of Operations Research

, Volume 181, Issue 1, pp 485–501 | Cite as

A method for solving the general parametric linear complementarity problem

  • Zukui Li
  • Marianthi G. IerapetritouEmail author


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.


Parametric linear complementarity problem Minimum norm solution Mixed integer programming Multiparametric programming 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dept. of Chemical and Biochemical EngineeringRutgers UniversityPiscatawayUSA

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