Dual-feasible functions for integer programming and combinatorial optimization: Algorithms, characterizations, and approximations

Within the framework of the superadditive duality theory of integer programming, we study two types of dual-feasible functions of a single real variable (Alves et al., 2016). We introduce software that automates testing piecewise linear functions for maximality and extremality, enabling a computer-based search. We build a connection to cut-generating functions in the Gomory-Johnson and related models, complete the characterization of maximal functions, and prove analogues of the Gomory-Johnson 2-slope theorem and the Basu-Hildebrand-Molinaro approximation theorem. (c) 2019 Elsevier B.V. All rights reserved.