Optimal traffic engineering via Newton´s method

Recently, it has been proven that the minimum-cost multicommodity flow can be realized by a link-state routing protocol, PEFT, using uneven traffic splitting (D. Xu et al., 2008). The achievement is due to solving a new convex optimization problem, network entropy maximization (NEM), by a gradient descent algorithm. However, gradient descent algorithms are notorious for slow convergence to optimality whereas Newton´s method usually converges much faster. Solving NEM by Newton´s method is neither trivial nor standard because of the infinite number of variables NEM has. In this paper, we develop efficient Newton methods for the NEM problem.