In this paper, we employ the infinite dimensional state-space (IDEAS) paradigm to determine the globally minimum plate area for a liquid/vapor equilibrium based separation process (distillation) network. The IDEAS paradigm results in a convex (linear) optimization problem which accounts for all possible design alternatives. The obtained solution is thus guaranteed to be the global optimum over all networks. The power of the IDEAS paradigm is demonstrated in a case study on the separation of a nitrogen/oxygen mixture. The plate area for the IDEAS design is 58% lower than the plate area of the best conventional design.