MPEC problem formulations and solution strategies with chemical engineering applications

With the development and widespread use of large-scale nonlinear programming (NLP) tools for process optimization, there has been an associated application of NLP formulations with complementarity constraints in order to represent discrete decisions. Also known as mathematical programs with equilibrium constraints (MPECs), these formulations can be used to model certain classes of discrete events and can be more efficient than a mixed integer formulation. However, MPEC formulations and solution strategies are not yet fully developed in process engineering. In this study, we discuss MPEC properties, including concepts of stationarity and linear independence that are essential for well-defined NLP formulations. Nonlinear programming based solution strategies for MPECs are then reviewed and examples of complementarity drawn from chemical engineering applications are presented to illustrate the effectiveness of these formulations.