Convexification techniques for linear complementarity constraints

Trang T. Nguyen, Mohit Tawarmalani, Jean Philippe P. Richard

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationInteger Programming and Combinatoral Optimization - 15th International Conference, IPCO 2011, Proceedings
Number of pages13
StatePublished - Jul 11 2011
Externally publishedYes
Event15th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2011 - New York, NY, United States
Duration: Jun 15 2011Jun 17 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6655 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other15th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2011
CountryUnited States
CityNew York, NY

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