Journal of Optimization Theory and Applications

, Volume 140, Issue 2, pp 233–238 | Cite as

EP Theorem for Dual Linear Complementarity Problems



The linear complementarity problem (LCP) belongs to the class of \(\mathbb{NP}\) -hard problems. Therefore, we cannot expect a polynomial time solution method for LCPs without requiring some special property of the matrix of the problem. We show that the dual LCP can be solved in polynomial time if the matrix is row sufficient; moreover, in this case, all feasible solutions are complementary. Furthermore, we present an existentially polytime (EP) theorem for the dual LCP with arbitrary matrix.


Linear complementarity problem Dual LCP Row sufficient matrix *-matrix EP theorem 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Management ScienceStrathclyde UniversityGlasgowUK
  2. 2.Department of Operation ResearchEötvös Lorànd University of ScienceBudapestHungary
  3. 3.Department of Computing and SoftwareSchool of Computational Engineering and Science, McMaster UniversityHamiltonCanada

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