Many decision problems arising in engineering, science and operations research can be modeled as nonlinear optimization problems. Equilibrium constraints in the form of complementarity conditions often appear as constraints in these problems. This gives rise to Mathematical Programs with Equilibrium Constraints (MPECs).
Applications of equilibrium constraints are widespread and fast growing. Economic applications include inverse pricing, taxation models and traffic network design models. Engineering applications include the design of structures involving friction, elasto-hydrodynamic lubrication. Application in chemical engineering include phase equilibrium and flow through pipe networks. A new application of MPECs is emerging in VLSI chip placement, where complementarity models linear wire length.
Until recently, it had been assumed that equilibrium constraints cannot be solved satisfactorily with standard nonlinear optimization solvers. Both numerical and theoretical evidence has been advanced which support this view. As a consequence, MPECs were widely regarded as ill-conditioned and ill-posed problems.
Despite this gloomy outlook, new practical experience indicates that MPECs can be solved efficiently using certain standard solvers. The excellent practical performance of these methods is no accident and can be explained rigorously, providing new theoretical insight into MPECs. This insight is also exploited to explain why other methods are much less robust and develop modifications for these methods.
The overall aim of this research is to provide robust and efficient solver with proven convergence properties for large scale MPECs. The ready availability of such solvers will drive novel applications of complementarity problems.
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