Direct search methods for an open problem of optimization in systems and control

The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix inequality algorithm (ILMI) has been proposed recently. As it often happens, this algorithm does not have guaranteed global convergence and therefore many methods may perform better. We will put forward how some general purpose optimization solvers are more suited than the ILMI. This is illustrated with the considered problem and example, but the general observations remain valid for many similar situations in the literature.