There is growing interest in statistical inference under order restrictions. A major demand in this subject is to have a fast, direct method to solve the least squares problem of partially ordered isotonic regression. The Min-Max algorithm is such a method in which the user searches for the global minimum and the local maximum successively. A comparison of algorithms for partially ordered isotonic regression is included. As an application, using this efficient algorithm, it is feasible to approximate critical values of isotonic tests by simulation.
"The Min-Max Algorithm and Isotonic Regression." Ann. Statist. 11 (2) 467 - 477, June, 1983. https://doi.org/10.1214/aos/1176346153