Function minimization by conjugate gradients

By R. Fletcher, C. M. Reeves. 1964

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

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Citations in the corpus

SGDR: Stochastic Gradient Descent with Warm Restarts (2016, background): “Fletcher & Reeves (1964) proposed to ﬂesh the history of conjugate gradient method every n or ( n + 1) iterations.”
Conjugate Gradient Methods with Armijo-type Line Searches (2002, methodology): “Several famous formulas for βk are called the Fletcher-Reeves (FR), Polak-Ribi´ ere-Polyak (PRP), Hestenes-Stiefel (HS), and conjugate descent (CD) formulas (see [9, 10 ,13,17,18]), and are given by”
Numerical Methods for Electronic Structure Calculations of Materials (2010, methodology): “Seven of the met hods are: the Hestenes and Stiefel method (HS) [72], the Fletcher-Reeves method (FR) [50], Danie l’s method (D) [34], the method by Polak, Ribiere, and Polyak (PRP) [135,136], the Conjugate Desc ent method by Fletcher (CD) [48], the Liu and Storey method (LS) [101], and the method b”
A neural network approach for attenuation relationships: An application using strong ground motion data from Turkey (2007, methodology): “Fletcher and Reeves (1964) introduced the nonlinear conjugate gradient method and proposed a formula to compute the scalar βk that it is called as Fletcher–Reeves conjugate gradient formula by the equation of, bk ¼ jjgk jj2 jjgk 1jj2 ð4Þ or in an update form, bk ¼ gTk gk gTk 1gk 1 ð5Þ where ||·||…”
A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence (2006, unknown): “Well-known conjugate gradient methods include the Fletcher–Reeves (FR) method (Fletcher & Reeves, 1964), the Polak–Ribière–Polyak (PRP) method (Polak & Ribiere, 1969; Polyak, 1969), the Hestenes– Stiefel (HS) method (Hestenes & Stiefel, 1952), the Dai–Yuan method (Dai & Yuan, 2000) and the…”
On Restart Procedures for the Conjugate Gradient Method (2004, methodology): “Two well-known formulas for βk are those of Fletcher–Reeves [9], Polak–Ribière [14] and Polyak [15] given by”
A modified Fletcher-Reeves-Type derivative-free method for symmetric nonlinearequations (2011, methodology): “The MFR method is a modification to the well-known Fletcher-Reeves (FR) [8] method for solving optimization problems.”
Two-dimensional velocity macro model estimation from seismic reflection data by local differential semblance optimization: applications to synthetic and real data sets (2001, methodology): “Among the multiple local optimization algorithms, we used a conjugate gradient method (Fletcher & Reeves 1964) for the optimization process.”
Full waveform inversion strategy for density in the frequency domain (2012, methodology): “The conjugate-gradient method (Fletcher & Reeves 1964) is employed to optimize the gradient direction.”