Advanced nonlinear programming (NLP) strategies based on equation-oriented (EO) process models are leading to significant improvements in computer-aided process engineering. The EO paradigm allows the development of large, integrated optimization platforms that expand the scope of continuous optimization tasks in process engineering. In particular, these platforms deploy significantly faster NLP strategies than in commercial simulation tools. Moreover, they exploit exact derivatives and system structure in order to consider much larger and more challenging systems. Finally, they allow the incorporation of much more general models, such as multi-level optimization and complementarity constraints. For process optimization this allows the treatment of extended models for complex phase equilibrium and process separations. These advances facilitate the optimization of novel integrated systems that arise in process intensification. Several separation case studies are presented that illustrate these optimization concepts and demonstrate their effectiveness for hybrid membrane/distillation separations and reactive distillation systems that typify novel systems in process intensification.