There are actually even so some crucial subclasses of IP and MIP difficulties which can be successfully solvable, most notably issues the place the constraint matrix is totally unimodular and the correct-hand sides with the constraints are integers or – far more normal – exactly where the method has the whole dual integrality (TDI) house.
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Linear programming problems is usually converted into an augmented variety so that you can apply the common type of the simplex algorithm.
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