Large-scale optimization: algorithm design and analysis

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Mathematical optimization arises in a wide range of science and engineering disciplines. It can be used by engineers to design systems that are "best" in some sense; it can be used by scientists in many fields to find the best model of a given physical process. The goal of optimization is to minimize (or maximize) an objective function while satisfying certain constraints. Applications often give rise to optimization problems with significant structure, which can be exploited to efficiently optimize models with huge numbers of variables. This proposal describes a five-year research program to develop fundamental theoretical tools in optimization and innovative algorithms for solving large-scale problems of practical interest. The proposal addresses issues in algorithm development, analysis, and implementation. It involves the development of general-purpose algorithms as well as of specialized optimization methods for particular applications. In many contexts, optimization is a vital step in a larger procedure; it is therefore critical that optimization algorithms be fast and reliable. Advances in efficiency and robustness are welcomed by optimization users in industry and academia. The proposed research will have an impact on three groups: researchers in optimization, researchers in specific application fields, and industry practitioners.