This work investigates some of the quantities indicating the degree of robustness of a dynamical system; all intrinsically have ties with the sensitivity of the eigenvalues. The emphasis is put on the computation of these quantities rather than further analysis of their effectiveness in indicating the robustness. The algorithms devised benefit from equivalent singular-value or eigenvalue optimization characterizations. The difficulty that we attempt to overcome is the nonconvex nature of these optimization problems. Surprisingly the global extrema of these nonconvex problems are located reliably and with a decent amount of work (usually by means of a fast converging algorithm with a cubic cost at each iteration) by the help of structured eigenvalue solvers and iterative eigenvalue solvers.
Emre Mengi received his Ph.D. from Courant Institute, New York University in 2006. He held an S.E.W. assistant professorship position at UC San Diego before joining to Koc University in Istanbul, where he is currently an assistant professor in mathematics. Emre Mengi's research concerns numerical optimization and perturbation theory of eigenvalues.