Alternatives with stronger convergence than coordinate-descent iterative LMI algorithms

TL;DR

This paper highlights the limitations of coordinate-descent iterative LMI algorithms for non-convex problems and advocates for alternative methods with better convergence guarantees and practical efficiency.

Contribution

It emphasizes the need to adopt more effective optimization techniques for non-convex problems in systems and control, providing comparisons and an illustrative example.

Findings

Coordinate-descent algorithms often yield suboptimal solutions.

Alternative optimization methods can offer better convergence guarantees.

Practical efficiency of these alternatives is demonstrated through an example.

Abstract

In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other optimization methods better equipped to deal with such problems (having theoretical convergence guarantees and/or being more efficient in practice). This fact, already outlined at several places in the literature, still appears to be disregarded by a sizable part of the systems and control community. Thus, main elements on this issue and better optimization alternatives are presented and illustrated by means of an example.