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Rosenbrock Function
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical optimization, the Rosenbrock function is a non-convex function used as a performance test problem for optimization algorithms. It is also known as Rosenbrock''s valley or Rosenbrock''s banana function. The global minimum is inside a long, narrow, parabolic shaped flat valley. To find the valley is trivial. To converge to the global minimum, however, is difficult. It is defined by f(x, y) = (1-x)^2 + 100(y-x^2)^2 .quad. It has a global minimum at (x,y) = (1,1) where f(x,y) = 0. A different coefficient of the second term is sometimes given, but this does not affect the position of the global minimum. Two variants are commonly encountered. One is the sum of N / 2 uncoupled 2D Rosenbrock problems, f(x1, x2, dots, xN) = sum{i=1}^{N/2} left[100(x{2i-1}^2 - x{2i})^2 + (x{2i-1} - 1)^2 right]. This variant is only defined for even N and has predictably simple solutions. A more involved variant is f(x) = sum{i=1}^{N-1} left[ (1-xi)^2+ 100 (x{i+1} - x_i^2 )^2 right] quad forall xinmathbb{R}^N.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131256035
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131256035
- Format Fachbuch
- Titel Rosenbrock Function
- Herausgeber Betascript Publishing
- Anzahl Seiten 76
- Genre Mathematik
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