Before revision: Given a separation oracle SO for a convex function f that has an integral minimizer inside a box with radius R, we show how to efficiently find a minimizer of f using at most  O(n (n + \log(R))) calls to SO (n, \log(R)) arithmetic operations, or (b) O(n \log(nR)) calls to SO and \exp(n) \cdot poly(\log(R)) arithmetic operations} .
After revision: Given a separation oracle SO for a convex function f that has an integral minimizer inside a box with radius R, we show how to find an exact minimizer of f using at most O(n (n + \log(R))) calls to SO (n, \log(R)) arithmetic operations, or (b) O(n \log(nR)) calls to SO and \exp(n) \cdot poly(\log(R)) arithmetic operations} .