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Fitting piecewise linear continuous functions |
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| Authors: | Alejandro Toriello Juan Pablo Vielma |
| Institution: | a Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, 3715 McClintock Avenue, GER 240, Los Angeles, CA 90089, United States b Department of Industrial Engineering, 1048 Benedum Hall, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA 15261, United States |
| Abstract: | We consider the problem of fitting a continuous piecewise linear function to a finite set of data points, modeled as a mathematical program with convex objective. We review some fitting problems that can be modeled as convex programs, and then introduce mixed-binary generalizations that allow variability in the regions defining the best-fit function’s domain. We also study the additional constraints required to impose convexity on the best-fit function. |
| Keywords: | Integer programming Quadratic programming Data fitting/regression Piecewise linear function |
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