In this section we apply the developed methods to two examples. In a first example we optimize a column with a simple dividing wall splitting a ternary mixture. We will compare the results with Aspen Plus R and show that our implementation is very close to the implementation of Aspen Plus R . The second example is more challenging, since it is about the separation of a quaternary mixture. We demand higher purities and consider two dividing walls. For this example the benefits of the new method become more apparent.