rosenbrock function mathematical optimization (2 Ergebnisse)

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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(x_1, x_2, dots, x_N) = 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-x_i)^2+ 100 (x_{i+1} - x_i^2 )^2 right] quad forall xinmathbb{R}^N.

Taschenbuch. Zustand: Neu. Rosenbrock Function | Mathematical Optimization, Convex Function, Algorithm, Optimization, Sturm's Theorem | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786131256035 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.