1. A method for estimating nonlinear noise in optical transport networks for optical paths, the method comprising: identifying a candidate path in an optical transport network, the candidate path comprising K number of nodes designated 1 to K; for each value of a positive integer k such that (1<k<K): based on a spectral inversion node functional at node k, calculating a first value based on nonlinear transfer function integrals for each link from node 1 to node k, the first value representing nonlinear noise in links before the spectral inversion node along the candidate path, calculating the first value includes: retrieving nonlinear transfer function integral values for each link from node 1 to node k, adding an accumulated term for phase shift by dispersion to each of the integral values for each link from node 1 to node k, concatenating the integral values for each link from node 1 to node k, multiplying the concatenated integral values by a phase shift exponential term corresponding to a dispersion compensation module located at the spectral inversion node, and phase conjugating the integral values for each link from node 1 to k; calculating a second value based on nonlinear transfer function integrals for each link from node k to node K, the second value representing nonlinear noise in links after the spectral inversion node along the candidate path; and adding the first value and the second value to obtain a third value as a function of k; and selecting the value of k based on the third value, wherein the spectral inversion node is placed at node k in the candidate path.