A sub-additive DC approach to the complementarity problem

  • L. Abdallah
  • M. Haddou
  • T. MigotEmail author


In this article, we study a merit function based on sub-additive functions for solving the non-linear complementarity problem (NCP). This leads to consider an optimization problem that is equivalent to the NCP. In the case of a concave NCP this optimization problem is a Difference of Convex (DC) program and we can therefore use DC Algorithm to locally solve it. We prove that in the case of a concave monotone NCP, it is sufficient to compute a stationary point of the optimization problem to obtain a solution of the complementarity problem. In the case of a general NCP, assuming that a DC decomposition of the complementarity problem is known, we propose a penalization technique to reformulate the optimization problem as a DC program and prove that local minima of this penalized problem are also local minima of the merit problem. Numerical results on linear complementarity problems, absolute value equations and non-linear complementarity problems show that our method is promising.


Complementarity problem Difference of convex Merit function DC algorithm 

Mathematics Subject Classification

90C59 90C30 90C33 65K05 49M20 



The authors would like to thank anonymous referees for their helpful remarks and comments.


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Authors and Affiliations

  1. 1.Lebanese UniversityTripoliLebanon
  2. 2.INSA Rennes, CNRS, IRMAR - UMR 6625Univ RennesRennesFrance
  3. 3.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada

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