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

A Comparison of Nonsmooth, Nonconvex, Constrained Optimization Solvers for the Design of Time-Delay Compensators