# Tightening Discretization-based MILP Models for the Pooling Problem using Upper Bounds on Bilinear Terms

arXiv: https://arxiv.org/abs/2207.03699 · HTML: https://mlsanity.com/paper/2207.03699/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 36 references that are in the map.
- First posted on arXiv 8 Jul 2022.

## Builds on (most cited first, 4 of 4)

- [An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs](https://mlsanity.com/paper/1707.02514/) (2017)
- [Strong Convex Nonlinear Relaxations of the Pooling Problem](https://mlsanity.com/paper/1803.02955/) (2018)
- [Convex Hull Representations for Bounded Products of Variables](https://mlsanity.com/paper/2004.07233/) (2020)
- [Solving the pooling problem at scale with extensible solver GALINI](https://mlsanity.com/paper/2105.01687/) (2021)

## Abstract (arXiv)

Discretization-based methods have been proposed for solving nonconvex optimization problems with bilinear terms such as the pooling problem. These methods convert the original nonconvex optimization problems into mixed-integer linear programs (MILPs). In this paper we study tightening methods for these MILP models for the pooling problem, and derive valid constraints using upper bounds on bilinear terms. Computational results demonstrate the effectiveness of our methods in terms of reducing solution time.