αΒΒ
"Alpha BB" redirects here. For other uses, see ABB (disambiguation).
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.
References
This article is issued from Wikipedia - version of the Wednesday, March 23, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.