Robust optimal experiment design for dynamic system identification is cast as a minmax optimization problem, which is infinite-dimensional. If the input spectrum is discretized (either by considering a Riemmann approximation, or by restricting it to the span of a finite dimensional linear space), this problem falls within the class of semi-infinite convex programs. One approach to this optimization problem of infinite constraints is the so called "scenario approach", which is based on a probabilistic description of the uncertainty to deliver a finite program that attempts to approximate the optimal solution with a prescribed probability. In this paper, we propose as an alternative an exchange algorithm based on some recent advances in the field of semi-infinite programming to tackle the same problem. This method is compared with the scenario approach both from the aspects of accuracy and computational efficiency. Furthermore, the comparison includes the MATLAB semi-infinite solver fseminf to provide a general palette of methods approximating the robust optimal design problem.