How to project onto the monotone nonnegative cone using Pool Adjacent   Violators type algorithms
  The metric projection onto an order nonnegative cone from the metric projection onto the corresponding order cone is derived. Particularly, we can use Pool Adjacent Violators-type algorithms developed for projecting onto the monotone cone for projecting onto the monotone nonnegative cone too. 
A. B. N\'emeth and S. Z. N\'emeth
math.ST math.OC stat.TH