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Most branch-and-bound algorithms in global optimization depend on convex underestimators to calculate lower bounds of a minimization objective function. The αBB methodology produces such underestimators for sufficiently smooth functions by analyzing interval Hessian approximations. Several methods to rigorously determine the αBB parameters have been proposed, varying in tightness and computational complexity. We present new polynomial-time methods and compare their properties to existingdoi:10.1007/s10898-013-0057-y fatcat:fenxrv2tmfgnxcd3hahlh4tzqm