Isotonic regression techniques are reinterpreted and extended to include upper
and lower bounds on the ordered sequences in question. This amounts to solving
the shortest distance problem for the order simplex $$S^n = \{ t \in R^n :0
\leqslant t_1 \leqslant t_2 \leqslant \cdots \leqslant t_n \leqslant 1\} $$ inR
n . AnO(n) algorithm is presented for this problem, verified via the Kuhn-Tucker
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