A Note on the Asymptotic Theory of Integer Programming and the 0-1 Case.

While asymptotic theory is in many ways useful for 0-1 problems too, in this note the author shows that in the case of a 0-1 program the sufficient condition given by Gomory for a solution to the asymptotic problem to solve the initial integer program, is never satisfied. A much weaker and less than sufficient condition is also never satisfied. This underscores the need to use information about the constraints that are slack at the linear programming optimum. Author