We present a special application of optimization techniques, based on Interior Point methods, in order to cope with the general Constrained Simulation Problem (CSP). A Successive Linear Programming (SLP)method or a Successive Quadratic Programming (SQP) method are alternatively exploited to treat in a robust and efficient way the process simulation problems that are, in general, subject to inequalities to be strictly satisfied. The methods are tested on a large-scale example concerning a Petlyuk distillation scheme for the separation of the Benzene-Toluene-Xylene (BTX) ternary mixture. The model exhibits a rather complex behaviour with infeasible set of specifications as well as multiple solutions for its 5 degrees of freedom.