  We present a detailed set of performance comparisons of two state-of-the-art
solvers for the application of designing time-delay compensators, an important
problem in the field of robust control. Formulating such robust control
mechanics as constrained optimization problems often involves objective and
constraint functions that are both nonconvex and nonsmooth, both of which
present significant challenges to many solvers and their end-users hoping to
obtain good solutions to these problems. In our particular engineering task,
the main difficulty in the optimization arises in a nonsmooth and nonconvex
stability constraint, which states that the infinite spectrum of zeros of the
so-called shaper should remain in the open left half-plane. To perform our
evaluation, we make use $\beta$-relative minimization profiles, recently
introduced visualization tools that are particularly suited for benchmarking
solvers on nonsmooth, nonconvex, constrained optimization problems.
Furthermore, we also introduce new visualization tools, called Global-Local
Profiles, which for a given problem and a fixed computational budget, assess
the tradeoffs of distributing the budget over few or many starting points, with
the former getting more budget per point and latter less.
