We address the determination of globally optimal solutions for a class of dynamic systems with highly nonlinear behavior. Specifically, to determine optimal transition trajectories between steady-state operating points, we consider the impact of output multiplicities in obtaining multiple optima around regions featuring severe nonlinearities. For dynamic optimization, we found that current global optimization solvers tend to demand much more computational effort when compared to local optimization solvers. Therefore, with appropriate variable bounds, good initialization strategies, and, if necessary, multiple restart strategies, local optimization solvers are often competitive, in terms of CPU time, when faced with the decision of finding global optimal solutions. Moreover, while the presence of output multiplicities does not seem to be strictly necessary for multiple local optima, we find that nonunique solutions may emerge for transitions around nonlinear regions. In order to quantify the presence of multiple local optima, we propose an empirical indicator that seems able to predict the potential for the emergence of unique optimal solutions.