Parallel Computing for Large-Scale Optimization

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Large-scale optimization problems arise in a great variety of important scientific, engineering, and economic applications, and exhibit structures that allow solution via algorithms that possess a high degree of parallelism. Research will be continued in the development of decomposition algorithms appropriate for the distributed solution of such problems and in the implementation and testing of these methods on a variety of parallel architectures including the multicomputers and multiprocessors available at the Computer Sciences Department and those available elsewhere via ARPANET. Such algorithms have the large granularity and low data transfer properties that are ideally suited to parallel architectures. Particular emphasis will be given to network optimization problems, since a large proportion of the most difficult real-world applications of mathematical programming fall into this category, and since such problems also cover a broad spectrum of mathematical classes (from linear to nonlinear, from convex to nonconvex, from deterministic to stochatic). The development of parallel algorithms for these problems will also require the development of scheduling and load-balancing techniques that will be useful in the study of distributed techniques for other areas of large- scale scientific computation. The decomposition of problems to run simultaneously on multiple parallel processors is essential if these new architectures are to be effectively used.