Abstract
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 language | English (US) |
---|---|
Title of host publication | Integer Programming and Combinatoral Optimization - 15th International Conference, IPCO 2011, Proceedings |
Pages | 336-348 |
Number of pages | 13 |
DOIs | |
State | Published - 2011 |
Externally published | Yes |
Event | 15th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2011 - New York, NY, United States Duration: Jun 15 2011 → Jun 17 2011 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|
Volume | 6655 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Other
Other | 15th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2011 |
---|---|
Country/Territory | United States |
City | New York, NY |
Period | 6/15/11 → 6/17/11 |
Bibliographical note
Funding Information:This work was supported by NSF CMMI grants 0856605 and 0900065.