Parallel Reliable Global Optimization with Interval Arithmetic

在这项建议的RUI研究中，我们将应用我们现有的研究成果来设计高效的并行算法，并开发软件来可靠地求解无约束和有约束的多变量全局非线性优化问题。为了获得高可靠性，即使在数据存在不确定性、舍入误差和有限位计算的非线性的情况下，我们也在这个项目中应用了区间算法。所用的基本算法是区间分枝定界法和区间牛顿/广义二分法，在设计并行算法和开发可移植软件时，我们将充分利用并行计算的优势，由于问题的空间性质，不仅可以大大减少计算时间，而且可以显著减少计算量。为了达到高效率，我们将通过处理器间的通信在可用处理器之间动态平衡工作负载。该软件将独立于体系结构。一般稀疏性和可伸缩性也将被考虑。研究成果、并行软件包、安装和用户指南以及测试实例将通过互联网免费传播。

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.