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Advances in Operations Research
Volume 2016, Article ID 5017369, 11 pages
Research Article

Certificates of Optimality for Mixed Integer Linear Programming Using Generalized Subadditive Generator Functions

1School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6
2Department of Computer Science, University of California, Davis, CA 95616, USA

Received 10 November 2015; Revised 17 May 2016; Accepted 18 July 2016

Academic Editor: Imed Kacem

Copyright © 2016 Kevin K. H. Cheung and Babak Moazzez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce generalized subadditive generator functions for mixed integer linear programs. Our results extend Klabjan’s work from pure integer programs with nonnegative entries to general MILPs. These functions suffice to achieve strong subadditive duality. Several properties of the functions are shown. We then use this class of functions to generate certificates of optimality for MILPs. We have performed a computational test study on knapsack problems to investigate the efficiency of the certificates.