The bounds were chosen in such a way that the intervals contain the values computed with the V min diagrams with and without the modifications. The random initial points are reasonable in the sense that concentrations are set to 0 which are expected to be close to 0 in a feasible solution, but otherwise the random initial values can vary very roughly and can be far away from a solution. With these new initial values we followed the two step procedure by first adding the inequalities given in Equations ( ) and ( ) and then solving the full optimization problem. We repeated this for 100 randomly chosen initial values. The results are summarized in Table . For each run, we checked whether the optimality conditions were met for the final values. The number of these runs divided by the total number of runs performed gives the success rate. We also collected the final objective value and the time needed for each successful run. As a comparison we used ten times the starting values proposed by the V min diagrams (orig. V min ) and the values obtained by the modification introduced by Ränger and Grützner 2021 (mod. V min ). As expected, due to the high non-linearity of the MESH equation, the calculations do not converge from all possible choices of initial values. However, the results show that even if the starting values are chosen randomly, convergence can be achieved for a majority of the test runs. The success rate with random initial values can be further increased with a multi start strategy. For example, the probability of not finding the optimal solution decreases to a value less than 0.01% for 3 independent repetitions. With all three different strategies, we found the same optimal solution. In fact, all successful runs converged to the same solution. This means that although the problem formulation is highly non-linear, no different local solutions were found. Despite the fact that convergence can often be achieved with random initial values, the use of good starting values is still beneficial. First, in our experiments, the good initial values always converged. Second, fewer iterations were needed, resulting in less computation time.