Convexification Techniques for Linear Complementarity Constraints
We develop convexification techniques for linear programs with linear complementarity constraints (LPCC). In particular, we generalize the reformulation-linearization technique of  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.
KeywordsConvex Hull Complementarity Problem Linear Constraint Linear Complementarity Problem Complementarity Constraint
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- 5.Hu, J., Mitchell, J.E., Pang, J.S., Yu, B.: On linear programs with linear complementarity constraints. Journal of Global Optimization (to appear)Google Scholar
- 11.Tawarmalani, M.: Inclusion certificates and disjunctive programming. presented in Operations Research Seminar at GSIA, Carnegie Mellon University (2006)Google Scholar
- 12.Tawarmalani, M.: Inclusion certificates and simultaneous convexification of functions. Mathematical Programming (2010) (submitted)Google Scholar