# Intersection cuts for factorable MINLP

## TL;DR

This paper introduces a novel method for constructing tight concave underestimators of factorable functions to generate effective intersection cuts for mixed-integer nonlinear programming, independent of domain bounds.

## Contribution

It presents a new procedure for creating domain-independent concave underestimators and extends strengthening techniques to improve intersection cuts in MINLP.

## Key findings

- Constructed tight concave underestimators for factorable functions.
- Developed a strengthening procedure exploiting domain bounds.
- Extended monoidal strengthening for integer variables.

## Abstract

Given a factorable function f, we propose a procedure that constructs a concave underestimator of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain. Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables.