While the upwards stage-to-stage calculations solve all MESH equations in the stages 1 to n s -1, the downwards calculations solve all equations in the stages n s + 1 to n. The equations corresponding to stage n s haven't been considered yet. Also Equation ( ) and ( ) that guarantee that the vapor or liquid outgoing streams of a split stage have the same concentrations are not yet considered. These equations are included in the optimization problem described at the beginning of this section and are solved by the optimization routine. After convergence of the optimization all MESH equations describing the multiple dividing wall column are fulfilled.