Alternatives with stronger convergence than coordinate-descent iterative LMI algorithms

TL;DR

This note aims 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.

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.