Arbitrarily tight BB underestimators of general non-linear functions over sub-optimal domains.

In this paper we explore the construction of arbitrarily tight BB relaxations of general non-linear non-convex functions. We illustrate the theoretical challenges of building such relaxations by deriving conditions under which it is possible for an BB underestimator to provide exact bounds. We subsequently propose a methodology to build BB underestimators which may be arbitrarily tight (i.