Abstract: The present invention is directed to a method for simulating and optimizing a plant model. The plant model having a multiplicity of equipment models for a desired processing plant and a multiplicity of local property models for the material components within the plant includes providing a set of initial values for each property model in a data storage area. A first set of coefficients in each property model is determined. A set of equations representing the equipment models and property models, wherein the property models having a complementarity formulation, are executed simultaneously by the digital processor by using the first set of coefficients to determine a second set of coefficients in each property model. The second set of coefficients are stored in the data storage area.