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,
including overall structure and basic techniques, with mathematically
rigorous packages. Nonetheless, it is not trivial to make non-rigorous
packages rigorous. In this talk we

1. Define different kinds of answers that global optimization software
can claim to provide.

2. Explain where rigor might be needed and where it is not practical.

3. Briefly review salient techniques in deterministic branch and bound
methods.

4. Illustrate pitfalls in non-rigorous branch and bound methods.

5. Outline some of the techniques to make non-rigorous software rigorous.