These consideration motivate to use a two step procedure. In a first step both inequalities given in Equations ( ) and ( ) are added to the optimization problem given in Equation ( ). During the optimization the up and downcalculations can always be performed. This means that all functions can be evaluated and the optimization routine can find a solution. As we have added two additional inequalities, the calculated solution is in general not optimal for the original problem without these two additional assumptions. This is why a second step is performed in which we solve the optimization problem without the additional inequalities. As a starting point we use the optimization variables calculated in the first step. These variables already satisfy all MESH equations and the up and down-calculations can be evaluated at this starting point. Whenever a point is reached for which any of the up and down-calculations fails a smaller step can be taken. This way the optimization routine stays close to a feasible point. In our experiments presented in Section 5 the approximation calculated in the first step was always already close to the overall optimal solution.