Constructing general dual-feasible functions

Dual-feasible functions have proved to be very effective for generating fast lower bounds and valid inequalities for integer linear programs with knapsack constraints. However, a significant limitation is that they are defined only for positive arguments. Extending the concept of dual-feasible function to the general domain and range RR is not straightforward. In this paper, we propose the first construction principles to obtain general functions with domain and range RR, and we show that they lead to non-dominated maximal functions.