Complex sentence: Nestrov and Nemirovskii came up with a special class of such barriers that can be used to encode any convex set and they guarantees that the number of iterations of the algorithm is bounded by a polynomial in the dimension and accuracy of the solution.
Split into simpler sentences: Nestrov and Nemirovskii came up with a special class of such barriers that can be used to encode any convex set. They guarantee that the number of iterations of the algorithm is bounded by a polynomial in the dimension and accuracy of the solution.