In this work, we employ a state space representation of a heat/mass exchanger network to derive a mathematical formulation of the minimum total annualized cost (TAC) problem. Mathematical properties of the resulting nonlinear program's global optimum are then derived, using a variation induced minimization (VIM) technique and control theoretic concepts. This technique successfully identifies variables which are zero at the global optimum, thus reducing the size of the optimization problem. It is established that, under certain conditions, all self-recycle and total network bypass flow rates can be chosen to be zero at the TAC minimum. Two heat exchange network (HEN) TAC synthesis problems are employed to illustrate the validity of these properties, as well as the importance of the conditions under which the properties are derived. A hybrid algorithm, which consists of branch and bound underestimation with imbedded interval analysis, is employed in identifying numerically the optimum of these TIEN TAC problems.