This paper is concerned with regression under a "sum" of partial order cons
traints, Examples include locally monotonic, piecewise monotonic, runlength
constrained, and unimodal and oligomodal regression, These are of interest
not only in nonlinear filtering but also in density estimation and chromat
ographic analysis, It is shown that under a least absolute error criterion,
these problems can be transformed into appropriate finite problems, which
can then be efficiently solved via dynamic programming techniques, Although
the result does not carry over to least squares regression, hybrid program
ming algorithms can be developed to solve least squares counterparts of cer
tain problems in the class.