Interval computations, rigour and non-rigour in deterministic continuous global optimization

Deterministic branch and bound methods for the solution of general nonlinear programs have become increasingly popular during the last decade or two, with increasing computer speed, algorithmic improvements, and multiprocessors. There are presently several commercial packages. Although such packages are based on exhaustive search, not all of them rigorously take account of roundoff error, singularities, and other possibilities. Popular non-rigorous packages have much in common with mathematically rigorous packages, including overall structure and basic techniques. Nonetheless, it is not trivial to make non-rigorous packages rigorous. We