Rigorous Global Optimization of System Parameters
AbstractIn 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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