A Collection of Challenging Optimization Problems in Science, Engineering and Economics

TL;DR

This paper introduces a new database of challenging nonlinear systems of equations and optimization problems from science, engineering, and economics, aiming to facilitate benchmarking and advancing solution methods.

Contribution

It initiates the creation of a comprehensive database of difficult SNEs and related optimization problems, including formulations, origins, and current results.

Findings

Provides a list of challenging SNE problems with mathematical formulations

Reviews computational approaches for solving SNEs and optimization problems

Aims to support benchmarking and research advancement in solution methods

Abstract

Function optimization and finding simultaneous solutions of a system of nonlinear equations (SNE) are two closely related and important optimization problems. However, unlike in the case of function optimization in which one is required to find the global minimum and sometimes local minima, a database of challenging SNEs where one is required to find stationary points (extrama and saddle points) is not readily available. In this article, we initiate building such a database of important SNE (which also includes related function optimization problems), arising from Science, Engineering and Economics. After providing a short review of the most commonly used mathematical and computational approaches to find solutions of such systems, we provide a preliminary list of challenging problems by writing the Mathematical formulation down, briefly explaning the origin and importance of the problem and giving a short account on the currently known results, for each of the problems. We anticipate that this database will not only help benchmarking novel numerical methods for solving SNEs and function optimization problems but also will help advancing the corresponding research areas.