Algebraic Constraints Implying Monotonicity for Cubics

Published

January 1, 2000

Author(s)

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

Abstract

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.

Citation

NIST Interagency/Internal Report (NISTIR) - 6453

Report Number

6453

NIST Pub Series

NIST Interagency/Internal Report (NISTIR)

Pub Type

NIST Pubs

Download Paper

https://doi.org/10.6028/NIST.IR.6453

Local Download

Keywords

constrained regression, monotonic regression, video quality measurement

Citation

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], https://doi.org/10.6028/NIST.IR.6453, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=17206 (Accessed April 25, 2024)