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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.

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Let G = (V, E) be a graph and let F be a family of subsets of V such thatThe minimum cardinality of an F-dominating of G is called the F-domination number of G and is denoted by γ F (G). In this paper we present several basic results on this parameter. We also introduce the concept of F-irredundance and obtain an inequality chain four parameters.

Correctness and efficiency of two algorithms by Burdet and Johnson (1975) and Klabjan (2007) for solving pure integer linear programming problems are studied. These algorithms rely on Gomory's corner relaxation and subadditive duality. Examples are given to demonstrate the failure of these algorithms on specific IPs and ways of I would also like to thank my committee members Dr.