Alternatives for optimization in systems and control: convex and non-convex approaches

TL;DR

This paper reviews current trends in systems and control optimization, highlighting the dominance of convex methods and advocating for non-convex approaches to better address complex problems.

Contribution

It provides an overview of optimization trends in systems and control and emphasizes the need to explore non-convex methods beyond the prevalent convex approaches.

Findings

Convex and LMI methods dominate current practices.

Non-convex problems are often overlooked despite their importance.

A new method to generate numerous research papers is proposed.

Abstract

In this presentation, we will develop a short overview of main trends of optimization in systems and control, and from there outline some new perspectives emerging today. More specifically, we will focus on the current situation, where it is clear that convex and Linear Matrix Inequality (LMI) methods have become the most common option. However, because of its vast success, the convex approach is often the only direction considered, despite the underlying problem is non-convex and that other optimization methods specifically equipped to handle such problems should have been used instead. We will present key points on this topic, and as a side result we will propose a method to produce a virtually infinite number of papers.