A novel method for the globally optimal solution of the general process network synthesis problem is first presented and then applied to the solution of the minimum utility cost (MUC) problem for mass exchange networks (MEN) with multicomponent targets (MT). Previous approaches that address the MUC MEN MT synthesis problem are discussed, and the novel conceptual framework, Infinite DimEnsionAl State-space (IDEAS), is then introduced. IDEAS allows the formulation of general process network synthesis problems as infinite convex (linear) programs whose local solutions are guaranteed to be globally optimal. In addition, an MUC MEN MT problem where conventional methods fail is probed. Then, the optimal network generated using IDEAS is discussed, together with the wide-ranging potential impact and flexibility of IDEAS.