Convexification Techniques for Linear Complementarity Constraints

  • Trang T. Nguyen
  • Mohit Tawarmalani
  • Jean-Philippe P. Richard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6655)


We develop convexification techniques for linear programs with linear complementarity constraints (LPCC). In particular, we generalize the reformulation-linearization technique of [9] to complementarity problems and discuss how it reduces to the standard technique for binary mixed-integer programs. Then, we consider a class of complementarity problems that appear in KKT systems and show that its convex hull is that of a binary mixed-integer program. For this class of problems, we study further the case where a single complementarity constraint is imposed and show that all nontrivial facet-defining inequalities can be obtained through a simple cancel-and-relax procedure. We use this result to identify special cases where McCormick inequalities suffice to describe the convex hull and other cases where these inequalities are not sufficient.


Convex Hull Complementarity Problem Linear Constraint Linear Complementarity Problem Complementarity Constraint 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Trang T. Nguyen
    • 1
  • Mohit Tawarmalani
    • 2
  • Jean-Philippe P. Richard
    • 1
  1. 1.Department of Industrial and Systems EngineeringUniversity of FloridaUSA
  2. 2.Krannert School of ManagementPurdue UniversityUSA

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