Algorithms for solving the isotonic regression problem in more than one dimension are difficult to implement because of the large number of lower sets present or because they involve search techniques which require a significant amount of checking and readjustment. Here a new algorithm for solving this problem based on a simple iterative technique is proposed and shown to converge to the correct solution.
"An Algorithm for Isotonic Regression for Two or More Independent Variables." Ann. Statist. 10 (3) 708 - 716, September, 1982. https://doi.org/10.1214/aos/1176345866