αΒΒ

αΒΒ is a second-order deterministic global optimization algorithm for finding the optima of general, twice continuously differentiable functions.^[1][2] The algorithm is based around creating a relaxation for nonlinear functions of general form by superposing them with a quadratic of sufficient magnitude, called α, such that the resulting superposition is enough to overcome the worst-case scenario of non-convexity of the original function. Since a quadratic has a diagonal Hessian matrix, this superposition essentially adds a number to all diagonal elements of the original Hessian, such that the resulting Hessian is positive-semidefinite. Thus, the resulting relaxation is a convex function.

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