Abstract
In this paper an extension of the classical problem of isotonic regression is first considered. This problem extends the criterion of minimizing convex functions by considering a more general situation. To solve this problem, the max–min formulae are extended by means of the concept of change-level vector, leading to new formulae and algorithms. Moreover, we will find explicit expressions for every isotonic regression when the solution is not unique by considering both max–min and change-level formulae. An immediate implication from the considered extension is that bounds for isotonic regressions can be stated. Furthermore, the problem of finding solutions within a horizontal band in the plane can now be solved. Finally, some practical applications are discussed.
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