  In this paper we describe active set type algorithms for minimization of a
smooth function under general order constraints, an important case being
functions on the set of bimonotone r-by-s matrices. These algorithms can be
used, for instance, to estimate a bimonotone regression function via least
squares or (a smooth approximation of) least absolute deviations. Another
application is shrinkage estimation in image denoising or, more generally,
regression problems with two ordinal factors after representing the data in a
suitable basis which is indexed by pairs (i,j) in {1,...,r}x{1,...,s}. Various
numerical examples illustrate our methods.
