Global Optimization for Algebraic Geometry – Computing Runge–Kutta Methods
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.
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