Section: New Results

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 R is not straightforward. In [10] , we propose the first construction principles to obtain general functions with domain and range $R$, and we show that they lead to non-dominated maximal functions.