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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 numerical analysis, a quasi-Newton method is an iterative numerical method used either to find zeroes or to find local maxima and minima of functions via an iterative recurrence formula much like the one for Newton's method, except using approximations of the derivatives of the functions in place of exact derivatives.
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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
However, the Nelder–Mead technique is a heuristic search method that can converge to non-stationary points [1] on problems that can be solved by alternative methods. [ 2 ] The Nelder–Mead technique was proposed by John Nelder and Roger Mead in 1965, [ 3 ] as a development of the method of Spendley et al. [ 4 ]