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A method for solving the general parametric linear complementarity problem
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DOI：10.1007/s10479-010-0770-6.png)
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This paper presents a solution method for the general (mixed integer) parametric linear complementarity problem pLCP(q(theta),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.
Keyword:
Parametric linear complementarity problem
Minimum norm solution
Mixed integer programming
Multiparametric programming
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