Equilibrium constraints in the form of complementarity conditions, and more generally variational inequalities, often appear as constraints in optimization problems. Applications of equilibrium constraints are widespread and fast growing. They cover very diverse areas such as the design of structures involving friction, elasto-hydrodynamic lubrication, taxation models, the modeling of competition in deregulated electricity markets and transportation network design.
Over recent years, it has become evident 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.
This talk starts by introducing and reviewing equilibrium constraints and gives some applications which emphasize the usefulness and elegance of equilibrium constraints as a modeling tool.
Next, we re-examine the assertion that standard techniques for NLP cannot be applied to equilibrium constraints and present some startling numerical evidence using our own NLP solver. The ultimate aim of this on-going work is the development of a robust solver for optimization problems with equilibrium constraints.
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