Mathematical Sciences: Algorithms for Mathematical Programming

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9414438 Goldfarb The objectives of this research are the development, analysis, and implementation of algorithms for solving mathematical programming problems. The focus of this project is on simplex algorithms, interior point algorithms and algorithms that combine interior point and multiplier penalty approaches, with particular emphasis on algorithms that are efficient both in theory and in practice. Specialized algorithms for network flow problems and those that take advantage of the architecture of massively parallel computers will be developed. Since many problems in science and engineering can be formulated as large-scale optimization problems, the development of efficient optimization algorithms under this project will have an impact on fields outside of optimization such as manufacturing (production planning and scheduling), biotechnology (protein folding), civil infrastructure (fleet and crew scheduling and transportation planning), and telecommunications (network design and routing) as well as on the field of optimization itself.