Computing Maximal Dual-feasible Functions Using a Novel Approach

Dual-feasible functions have been used in the broad area of combinatorial optimization to compute bounds and cutting planes for integer programming problems. These functions have been rediscovered recently, and studied in depth in different articles published in the literature. In this paper, we propose a new strategy for building families of staircase maximal dual-feasible functions using the properties of the dual solutions of a related linear programming problem. We describe the foundations of the strategy and we provide an example of a dual-feasible function generated in this way. Our study is completed by a comparison of this function with the best functions proposed in the literature.