Excluding Regions Using Sobol Sequences in an Interval Branch-and-Prune Method for Nonlinear Systems

Traditional rejection/reduction tests used in branch-and-prune methods for nonlinear systems usually are based on various forms of the interval Newton operator and constraint propagation techniques. Hence, they are relatively costly. This paper considers an additional phase of a branchand-prune method for the exclusion of regions not containing any solutions. Low-discrepancy sequences of Sobol are used to locate such regions, together with solving the interval tolerance problem and ε-inflation. Parallelization using the TBB library is also considered, and some numerical results are presented.