The well-known alpha BB method solves very general smooth nonconvex optimization problems. The algorithm works by replacing nonconvex functions with convex underestimators. The approximations are improved by branching and bounding until global optimality is achieved. Applications are abundant in engineering and science. We present a convex formulation in which the underestimators are improved without directly splitting the domain in a branch-and-bound tree. We show two illustrative examples and discuss some possible gains and drawbacks with the algorithm.