Merits of the Incremental Method for modeling Piecewise Linear functions

TL;DR

This paper enhances the incremental method for modeling piecewise linear functions, making it suitable for discontinuous cases and improving computational efficiency in optimization problems.

Contribution

The authors modify the incremental method for discontinuous PWL functions and introduce a tighter formulation for optimization with binary indicators.

Findings

Modified incremental method reduces computational time

Significant variable reduction achieved

Tighter formulation improves optimization efficiency

Abstract

Several techniques were proposed to model the Piecewise linear (PWL) functions, including convex combination, incremental and multiple choice methods. Although the incremental method was proved to be very efficient, the attention of the authors in this field was drawn to the convex combination method, especially for discontinuous PWL functions. In this work, we modify the incremental method to make it suitable for discontinuous functions. The numerical results indicate that the modified incremental method could have considerable reduction in computational time, mainly due to the reduction in the number of the required variables. Further, we propose a tighter formulation for optimization problems over separable univariate PWL functions with binary indicators by using the incremental method.