Equilibrium constraints in the form of complementarity conditions, and more generally variational inequalities, often appear as constraints in optimization problems, leading to MPECs (Mathematical Programs with Equilibrium Constraints). The talk starts by reviewing some new applications arising in chemical engineering.
Over recent years, it has been argued that equilibrium constraints cannot be solved satisfactorily with standard techniques for Nonlinear Programming (NLP). Both numerical and theoretical evidence has been advanced which support this view.
Surprisingly, our own numerical experience with over 100 MPECs suggests that certain NLP solvers can solve MPECs reliably and efficiently. This has led us to re-examine the standard arguments against NLP solvers. The talk concludes by presenting some recent theoretical insight into how and why some NLP solvers can solve MPECs, while others occasionally fail.