Parallel Reliable Global Optimization with Interval Arithmetic

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In this proposed RUI research, we will apply our current research results supported by NSFto design efficient parallel algorithms and to develop software to reliable numerical solutionsfor both unconstrained and constrained multivariate global nonlinear optimization problems.To achieve high reliability, even in the presence of uncertainty in the data, roundo error, andnonlinearities by finite digit computations, we apply interval arithmetic in this project. The basicalgorithms to be used are interval branch-and-bound method and interval Newton/generalizedbisection method.In designing parallel algorithm and developing portable software, we will take full advantagesof parallel computing to significantly reduce not only elapsed computation time but also totalamount of computation due to the spatial nature of the problem we address. To achieve high efficiency,we will balance workload dynamically among available processors through inter-processorcommunication. The software will be architecture independent. General sparsity and scalabilitywill be considered as well. The research results, parallel software package, installation and userguides, and testing examples will be freely disseminated through the Internet.