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The idea of Rosenbrock search is also used to initialize some root-finding routines, such as fzero (based on Brent's method) in Matlab. Rosenbrock search is a form of derivative-free search but may perform better on functions with sharp ridges. [6] The method often identifies such a ridge which, in many applications, leads to a solution. [7]
Nelder-Mead method applied to the Rosenbrock function. The Rosenbrock function can be efficiently optimized by adapting appropriate coordinate system without using any gradient information and without building local approximation models (in contrast to many derivate-free optimizers).
Exponential Rosenbrock methods were shown to be very efficient in solving large systems of stiff ordinary differential equations, usually resulted from spatial discretization of time dependent (parabolic) PDEs. These integrators are constructed based on a continuous linearization of (1) along the numerical solution
An interpretation of the Rosenbrock System Matrix as a Linear Fractional Transformation can be found in. [4] One of the first applications of the Rosenbrock form was the development of an efficient computational method for Kalman decomposition , which is based on the pivot element method.
Howard Rosenbrock was a pioneer of multivariable frequency domain control design methods. [6] He also made important contributions to the numerical solution of stiff differential equations and in the development of parameter optimization methods, both known as Rosenbrock methods .
Rosenbrock methods — derivative-free method, similar to Nelder–Mead but with guaranteed convergence; Augmented Lagrangian method — replaces constrained problems by unconstrained problems with a term added to the objective function; Ternary search; Tabu search
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In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as convergence rate, precision, robustness and general performance.