Before revision:  For the axis-aligned case, we formulate the problem for higher dimensions and present an exact optimization algorithm which solves the problem in \mathcal{O(d^3+d^2n) time, where d is the dimension and n is the number of inequalities defining the convex set.
After revision:  For the axis-aligned (d^3+d^2n) time, where d is the dimension and n is the number of inequalities defining the convex set.