Before revision:  The second part of our proposal is a k-step correction framework, which is proved to be able to convert any point within a small but fixed neighborhood of the true parameter value into an estimate that is asymptotically equivalent to GMM. Our result does not require the initial estimate to be consistent and only 2\log n iterations are needed . Since the k-step correction does not require any optimization, applying the k-step correction to MILP estimate provides a computationally attractive way of obtaining efficient estimators.
After revision:  The second part of our proposal is a k-step correction on an initial estimate. The initial estimate exploits the latest advances in mixed integer linear programming and can be computed within seconds. One theoretical contribution is that such initial estimators and Jacobian of the moment condition used in the k-step correction need not be even consistent and merely k=4\log n fast iterations are needed . Since the k-step correction does not require any optimization, applying the k-step correction to MILP estimate provides a computationally attractive way of obtaining efficient estimators.