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Quasi-Newton Method
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High Quality Content by WIKIPEDIA articles! In optimization, quasi-Newton methods (also known as variable metric methods) are well-known algorithms for finding local maxima and minima of functions. Quasi-Newton methods are based on Newton's method to find the stationary point of a function, where the gradient is 0. Newton's method assumes that the function can be locally approximated as a quadratic in the region around the optimum, and use the first and second derivatives (gradient and Hessian) to find the stationary point. In Quasi-Newton methods the Hessian matrix of second derivatives of the function to be minimized does not need to be computed. The Hessian is updated by analyzing successive gradient vectors instead. Quasi-Newton methods are a generalization of the secant method to find the root of the first derivative for multidimensional problems. In multi-dimensions the secant equation is under-determined, and quasi-Newton methods differ in how they constrain the solution, typically by adding a simple low-rank update to the current estimate of the Hessian.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130342944
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- Sprache Englisch
- Größe H220mm x B150mm x T12mm
- Jahr 2010
- EAN 9786130342944
- Format Kartonierter Einband
- ISBN 978-613-0-34294-4
- Titel Quasi-Newton Method
- Untertitel Maxima and Minima, Newton's Method in Optimization, Stationary Point, Hessian Matrix, Gradient, Argonne National Laboratory, Positive-Definite Matrix
- Gewicht 310g
- Herausgeber VDM Verlag Dr. Müller e.K.
- Anzahl Seiten 196
- Genre Mathematik
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