The inequalities above guarantee that for any choice of the optimization variables all calculated values for the concentrations are non-negative. There is a second possibility to ensure non-negative values. The equations used to derive the fixed point iterations hold for process variables that satisfy all MESH equations, including the equations that were added to the optimization problem. If we start with the corresponding optimization variables, the upwards an downwards calculations will reproduce the process variables. This means that for this optimization variables all values are non-negative. Now, as long as the upwards and downwards calculation are evaluated not too far away from process variables that satisfy all MESH equations, no negative values will occur.