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A characterization theorem is derived that motivates a procedure for generating discrete best monotonie approximations to n sequential data values, when a strictly convex objective function is used in the calculation. The procedure is highly useful in the discrete nonlinear optimization calculation that produces the best piecewise monotonie approximations to the data.doi:10.1090/s0025-5718-1990-1023046-3 fatcat:bf24cgefingthkha4s4xevwq2u