How good are interior point methods? Klee-Minty cubes tighten iteration-complexity bounds

By refining a variant of the Klee–Minty example that forces the central path to visit all the vertices of the Klee–Minty n-cube, we exhibit a nearly worst-case example for path-following interior point methods. Namely, while the theoretical iteration-complexity upper bound is O(2nn 5 2 ), we prove that solving this n-dimensional linear optimization problem requires at least 2n − 1 iterations.