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In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for optimization algorithms. [1] It is also known as Rosenbrock's valley or Rosenbrock's banana function. The global minimum is inside a long, narrow, parabolic-shaped flat ...
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]
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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.
It is recommended to name the SVG file “Rosenbrock roots exhibiting hump structures.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. Summary Description Rosenbrock roots exhibiting hump structures.pdf
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
If the constrained problem has only equality constraints, the method of Lagrange multipliers can be used to convert it into an unconstrained problem whose number of variables is the original number of variables plus the original number of equality constraints. Alternatively, if the constraints are all equality constraints and are all linear ...
The short form of the Rosenbrock system matrix has been widely used in H-infinity methods in control theory, where it is also referred to as packed form; see command pck in MATLAB. [3] An interpretation of the Rosenbrock System Matrix as a Linear Fractional Transformation can be found in. [4]