On the derivation of continuous piecewise linear approximating functions

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Abstract

We propose mixed-integer programming models for fitting univariate discrete data points with continuous piecewise linear (PWL) functions. The number of approximating function segments and the locations of break points are optimized simultaneously. The proposed models include linear constraints and convex objective function and, thus, are computationally more efficient than previously proposed mixed-integer nonlinear programming models. We also show how the proposed models can be extended to approximate univariate functions with PWL functions with the minimum number of segments subject to bounds on the pointwise error.

Original languageEnglish (US)
Pages (from-to)531-546
Number of pages16
JournalINFORMS Journal on Computing
Volume32
Issue number3
DOIs
StatePublished - Mar 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research

Keywords

  • Data fitting
  • Large-scale
  • Mixed-integer programming

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