Fitting piecewise linear continuous functions

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.