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Convexification techniques for linear complementarity constraints. (English) Zbl 1341.90130
Günlük, Oktay (ed.) et al., Integer programming and combinatoral optimization. 15th international conference, IPCO 2011, New York, NY, USA, June 15–17, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-20806-5/pbk). Lecture Notes in Computer Science 6655, 336-348 (2011).
Summary: We develop convexification techniques for linear programs with linear complementarity constraints (LPCC). In particular, we generalize the reformulation-linearization technique of [H. D. Sherali and W. P. Adams, SIAM J. Discrete Math. 3, No. 3, 411–430 (1990; Zbl 0712.90050)] 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.
For the entire collection see [Zbl 1216.90002].

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C05 Linear programming
90C11 Mixed integer programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
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