Cut-Generating Functions
Résumé
In optimization problems such as integer programs or their relaxations, one encounters feasible regions that are the inverse images of a specific closed set S by a linear mapping. One would like to generate valid inequalities that cut off infeasible solutions. Formulas for such inequalities can be obtained through cut-generating functions. This paper presents a formal theory of minimal cut-generating functions and maximal S-free sets which is valid independently of the particular S. This theory relies on tools of convex analysis.
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