We introduce a family of subadditive functions called Generator Functions for mixed integer linear programs. These functions were previously defined for pure integer programs with non-negative entries by Klabjan . They are feasible in the subadditive dual and we show that they are enough to achieve strong duality. Several properties of the functions are shown. We then use this class of functions for generating certificates of optimality for MILPs. We have done a test study on Knapsack problems to see how good the certificates can be.
Department of Computer Science, University of California, Davis, CA, USA. December 9 2014.