# Domain reduction techniques for global NLP and MINLP optimization

## TL;DR

This paper surveys domain reduction techniques used in NLP and MINLP optimization, analyzing their impact on solver performance through computational experiments on a large test set.

## Contribution

It provides a comprehensive review of domain reduction methods and evaluates their effectiveness across multiple global solvers on extensive test problems.

## Key findings

- Domain reduction techniques significantly improve solver convergence.
- Performance gains vary depending on problem characteristics.
- The survey highlights promising methods for future research.

## Abstract

Optimization solvers routinely utilize presolve techniques, including model simplification, reformulation and domain reduction techniques. Domain reduction techniques are especially important in speeding up convergence to the global optimum for challenging nonconvex nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) optimization problems. In this work, we survey the various techniques used for domain reduction of NLP and MINLP optimization problems. We also present a computational analysis of the impact of these techniques on the performance of various widely available global solvers on a collection of 1740 test problems.