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Computing valid inequalities for general integer programs using an extension of maximal dual feasible functions to negative arguments
Dual feasible functions (DFFs) were used with much success to compute bounds for several combinatorial
optimization problems and to derive valid inequalities for some linear integer programs. A major limitation of
these functions is that their domain remains restricted to the set of positive arguments. To tackle more general
linear integer problems, the extension of DFFs to negative arguments is essential. In this paper, we show how
these functions can be generalized to this case. We explore the properties required for DFFs with negative
arguments to be maximal, we analyze additional properties of these DFFs, we prove that many classical
maximal DFFs cannot be extended in this way, and we present some non-trivial examples.(undefined