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Does Mathematica offer any means for solving linear programming problems with "lazy constraints", as described e.g. here?

While I am not very familiar with linear programming, my understanding of the technique is the following:

  1. Solve the problem with only some of the constraints included.
  2. Identify a still not included constraint that is violated by the solution and provide it to the solver.
  3. Repeat from 1. until there are no more unsatisfied constraints left.

The solver is supposed to be able to re-use information from previous runs to achieve better performance. The technique should be useful when the total number of constraints is very large, so it is not practical to provide all of them at once.

If I try to naïvely re-run the LinearProgramming function with more and more constraints, of course it works, but the performance is not nearly as good as with other systems.

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