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Rigorous Global Optimization of System Parameters

Abstract

In this paper, after reviewing the basics of the method of Taylor models which enables rigorous computations, we introduced various function range bounding methods utilizing the inherent information associated to Taylor models. The superb performance is demonstrated by using a simple but tricky example. These components allow the construction of rigorous global optimization tools. We explain how to construct such a tool based on the branch-and-bound approach using the example function, while illustrating the excellent quality obtained by the method of Taylor models. With this, we proceed to demonstrate the efficiency by applying the method to a practical application to search all the parameter operation points yielding desired properties in a lattice of a charged particle storage ring.

K. Makino, M. Berz, Vestnik Mathematica 10,2 (2014) 61-71

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