Optimization techniques for modeling with piecewise-linear functions
Abstract
In this paper we aim to construct piecewise-linear (PWL) approximations for functions of multiple variables and to build compact mixed-integer linear programming (MILP) formulations to represent the resulting PWL function. On the one hand, we describe a simple heuristic to iteratively construct a triangulation with a small number of triangles, while decreasing the error of the piecewise-linear approximation. On the other hand, we extend known techniques for modeling PWLs in MILPs more efficiently than state-of-the-art methods permit. The crux of our method is that the MILP model is a result of solving some hard combinatorial optimization problems, for which we present heuristic algorithms. The effectiveness of our techniques is demonstrated by a series of computational experiments including a short-term hydropower scheduling problem
Cite
@article{arxiv.2503.10405,
title = {Optimization techniques for modeling with piecewise-linear functions},
author = {Péter Dobrovoczki and Tamás Kis},
journal= {arXiv preprint arXiv:2503.10405},
year = {2026}
}
Comments
28 pages, 10 figures, 11 tables, current version submitted to INFORMS Journal on Computing. Changes: Completely restructured document, extended theoretical analysis of the algorithm, added description of rank reduction heuristic, extended computational experiments, corrected typos. Note: Figures might be discoloured in Firefox