Penalty formulation for zero-one nonlinear programming

Raghavachari has shown the equivalence of zero-one integer programming and a concave quadratic penalty function for a sufficiently large value of the penalty. A lower bound for this penalty was found by Kalantari and Rosen. It was also shown that this penalty could not be reduced in specific cases. We show that the results generalize to the case where the objective function is any concave function. Equivalent penalty formulation for non-concave functions is also considered.