Applications, Algorithms and Extensions of Complementarity

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Over the past few years, several robust algorithms have been developed for solving nonlinear mixed complementarity problems, along with software aimed at making these algorithms accessible to researchers with applications that employ the complementarity framework. This proposal aims to continue and extend this work by considering the complete solution process for complementarity modeling in an interdisciplinary setting. The emphasis of the proposal is on developing new practical computational methods that will robustly solve the large-scale engineering and economic problems that will be formulated as part of this proposal in consultation with application experts. In contrast to much of the algorithm work that has been carried out to date, the solvers will be augmented with special purpose techniques that will attempt to automatically convert models to algorithmically advantageous forms and to diagnose deficiences in a given model. This will enable much quicker solution of many applications, since the solution time of an algorithm is typically much less that the time taken to develop, modify and refine the underlying models. It will be ensured that the algorithms and tools being developed are general purpose, easy to use and as informative to the user of the algorithms as possible. A direct interaction with experts in several application areas will determine how various physical phenomenon can be succinctly modeled using the notion of complementarity. As well as providing an automatic translation mechanism to convert nonlinear programs into mixed complementarity problems. The project will address the use of the complementarity framework for integrated assessment models in economics and fracture problems in structural engineering.