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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Global Optimization for Algebraic Geometry – Computing Runge–Kutta Methods
verfasst von : Ivan Martino, Giuseppe Nicosia
Erschienen in: Learning and Intelligent Optimization
Verlag: Springer Berlin Heidelberg
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This research work presents a new evolutionary optimization algorithm,
Evo-Runge-Kutta
in theoretical mathematics with applications in scientific computing. We illustrate the application of
Evo-Runge-Kutta
, a two-phase optimization algorithm, to a problem of pure algebra, the study of the parameterization of an algebraic variety, an open problem in algebra. Results show the design and optimization of particular algebraic varieties, the Runge-Kutta methods of order
q
. The mapping between algebraic geometry and evolutionary optimization is direct, and we expect that many open problems in pure algebra will be modelled as constrained global optimization problems.