Interfacing Optimization and Applications

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Modeling languages are heavily used in practice and therefore supply a critical vehicle for collaborative research in optimization. This project will faciliate this interaction by broadening the usage of optimization tools and environments in application areas. Due to the increasing demands in the size and complexity of applications, it has become vitally important for mathematical programmers to develop algorithms and tools within a modeling framework in order to advance the state-of-the-art in both applications and optimization. The thrust of the research will be in providing explicit examples of optimization technology, within targeted projects, and will address computational and tlieoretical aspects of large scale optimization in a practical setting.The new tools, environments, and algorithms of this proposal will enable an interactive approach to modeling with direct input from application and optimization experts during model development. The proposal will demonstrate such interactions within four application areas, namely the architectural design of video on-demand systems, cancer treatment plans in the context of tomotherapy, mathematical programming approaches to data mining, and the solution of complementarity problems arising in economics. A pivotal need is for visualization of optimization results within the application; a link between modeling languages and MATLAB will be provided for this purpose. An additional benefit of this link is the provision of a sophisticated mathematical programming capability to the MATLAB programniing environment.To address important issues and facets identified by domain experts, the resulting optimization problems are very large and require vast amounts of computing resources. Several new tools to enable the formulation and solution of such optimization problems on a metacomputer will be generated, all utilizing a pool of pre-existing, "off-the-shelf" workstations via Condor. A key component of the research will derive new algorithms that work within the proposed framework and exploit the metacomptiting resources. These include several new solvers for large scale complementarity problems and a fault tolerant parallel mixed integer programming solver.A fundamental goal of this effort is to educate researchers in other disciplines, primarily senior level undergraduates and graduate students, on the utility, use and power of these tools. Several of the application collaborations detailed in this proposal are direct consequences of interactions with colleagues and students during the first teaching of a course based on the topics of this project.