Over the past 20 years, PSA processes have gained increasing commercial acceptance as an energy-efficient separation technique. After a startup time, the system reaches cyclic steady state (CSS), at which the conditions in each bed at the start and end of each cycle are identical. Contrary to the traditional successive substitution method, we apply a direct determination approach using a Newton-based method with accurate sensitivities to achieve fast and robust convergence to CSS. Trust region methods and scaling are used to handle ill-conditioning and model nonlinearities. When design specifications are imposed, this approach is easily extended to include design constraints. This eliminates trial-and-error experiments and determines all the operating parameters simultaneously. In addition, we modify a standard flux limiter in order to deal with nondifferentiable terms and ensure computational accuracy and efficiency. Optimal PSA processes are designed by means of state-of-the-art rSQP-based optimization algorithms. The simultaneous tailored approach incorporates detailed adsorption models and specialized solution methods. Here, CSS convergence is achieved only at the optimal solution and the time-consuming CSS convergence loop is eliminated. Applications of several nonisothermal VSA O2 bulk gas separation processes are presented to illustrate all of these approaches.