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Algebraic Constraints Implying Monotonicity for Cubics



Charles D. Fenimore, John M. Libert, M. Brill


While it is straightforward to formulate constraints which ensure a cubic polynomial is monotonic on an interval, such constraints may not be in a form which is suitable for use in standard optimization software. The MATLAB package is typical; the required constraints are a series of simultaneous inequalities. Here we derive 2 algebraic inequalities which assure monotonicity of a cubic on an interval. The transformation to simultaneous constraints requires the application of basic logic. The constraints are applied to a problem which arose in analyzing data for an international comparison of video quality measurement computational models.
NIST Interagency/Internal Report (NISTIR) - 6453
Report Number


constrained regression, monotonic regression, video quality measurement


Fenimore, C. , Libert, J. and Brill, M. (2000), Algebraic Constraints Implying Monotonicity for Cubics, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online],, (Accessed May 30, 2024)


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Created December 31, 1999, Updated October 12, 2021