Alternatives with stronger convergence than coordinate-descent iterative LMI algorithms

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.Comment: 3 pages. Main experimental results reproducible from files available on http://www.mathworks.com/matlabcentral/fileexchange/33219 This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl