Parallel Reliable Global Optimization with Interval Arithmetic

University Of Central Arkansas, Conway AR

Investigators

Abstract

In this proposed RUI research, we will apply our current research results supported by NSF to design efficient parallel algorithms and to develop software to reliable numerical solutions for both unconstrained and constrained multivariate global nonlinear optimization problems. To achieve high reliability, even in the presence of uncertainty in the data, roundo error, and nonlinearities by finite digit computations, we apply interval arithmetic in this project. The basic algorithms to be used are interval branch-and-bound method and interval Newton/generalized bisection method. In designing parallel algorithm and developing portable software, we will take full advantages of parallel computing to significantly reduce not only elapsed computation time but also total amount 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-processor communication. The software will be architecture independent. General sparsity and scalability will be considered as well. The research results, parallel software package, installation and user guides, and testing examples will be freely disseminated through the Internet.