Direct search methods for an open problem of optimization in systems and control
For researchers in systems and control, this work demonstrates that simpler, general-purpose optimization methods can be more effective than specialized algorithms, though the findings are incremental.
The paper shows that general-purpose optimization solvers outperform a recently proposed iterative linear matrix inequality algorithm for a specific control problem, highlighting that many methods may perform better when global convergence is not guaranteed.
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.