Given a separation oracle SO for convex function f defined on ℝ n that has an integral minimizer inside box with radius R , we show how to find exact of using at most O(n (n log (n)/ (n) + ( ))) calls and poly )) arithmetic operations, or (nR) exp O(n) ) ⋅ (log (R) operations. When the set minimizers extreme points, our algorithm outputs . This improves upon previously best complexity 2 polynom...