TY - GEN

T1 - Convexification techniques for linear complementarity constraints

AU - Nguyen, Trang T.

AU - Tawarmalani, Mohit

AU - Richard, Jean Philippe P.

PY - 2011/7/11

Y1 - 2011/7/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79959971652&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-20807-2_27

DO - 10.1007/978-3-642-20807-2_27

M3 - Conference contribution

AN - SCOPUS:79959971652

SN - 9783642208065

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 336

EP - 348

BT - Integer Programming and Combinatoral Optimization - 15th International Conference, IPCO 2011, Proceedings

T2 - 15th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2011

Y2 - 15 June 2011 through 17 June 2011

ER -