A Rapidly Convergent Descent Method for Minimization

By Roger Fletcher, M. Powell. 1963

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Deep learning in neural networks: An overview (2014, neutral): “…1963; Newton, 1687; Schaback & Werner, 1992) and quasi-Newtonmethods (Broyden–Fletcher–Goldfarb–Shanno, BFGS) (Broyden et al., 1965; Fletcher & Powell, 1963; Goldfarb, 1970; Shanno, 1970) are computationally too expensive for large NNs. Partial BFGS (Battiti, 1992; Saito & Nakano, 1997)…”
A Survey of Optimization Methods From a Machine Learning Perspective (2019, background): “Then Fletcher and Powel [134] explained and improved this method, which sparked a lot of research in the late 1960s and early 1970s [6].”
Convergence Properties of the BFGS Algoritm (2002, methodology): “Another famous quasi-Newton method is the DFP method, which was discovered by Davidon [3] and modi(cid:12)ed by Fletcher and Powell [6].”
Restart procedures for the conjugate gradient method (1977, methodology): “The method of generating the parameters and the vector xl for the function (4.4) is described in reference [ 4 ].”
Optimum stacking sequence design of composite materials Part I: Constant stiffness design (2009, methodology): “The QN method by Davidon, Fletcher, and Powell (DFP) [13] is one of the most popular QN techniques used for composite layup design.”
UOBYQA: unconstrained optimization by quadratic approximation (2002, methodology): “The development of the UOBYQA software was guided by numerical experiments, using objective functions of the form F(x) = n X i=1 h b i ? n X j=1 (S ij sin x j + C ij cos x j ) i 2 ; x2R n : (6.1) The way of generating the parameters of F is taken from Fletcher and Powell (1963), and is as follows.”
Randomized Quasi-Newton Updates Are Linearly Convergent Matrix Inversion Algorithms (2016, methodology): “The BFGS update [4, 10, 12, 34] can be seen as a projection of A−1 onto a space of rank-2 symmetric matrices.”
Inferences from Cross-Sectional, Stochastic Frontier Models (2009, methodology): “After the OLS estimates have been obtained, a grid search procedure is used to find a starting value for γ; then these starting values are used in the DFP algorithm (Davidon, 1959; Fletcher and Powell, 1963).”
Learning deep similarity metric for 3D MR–TRUS image registration (2018, methodology): “istrations using the learned metric is also be demonstrated. DINO’s Learning Deep Similarity Metric for 3D MR-TRUS Registration 11 performance is contrasted with that of BFGS [16] and Powell’s method [5] without any prior solution space exploration. The results displayed in Table 1 show that using t”
On the capability of Monte Carlo and adjoint inversion techniques to derive posterior parameter uncertainties in terrestrial ecosystem models (2012, methodology): “A quasi-Newton method, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) variant of the Davidon-Fletcher-Powell (DFP) formula [Fletcher and Powell, 1963; Press et al., 1996], is used for the iterative minimization of the cost function, which requires the calculation of the gradient of J with respect to…”
Quasi-Newton Methods: A New Direction (2012, methodology): “Some of the most widely known members of this family include Broyden’s (1965) method, the SR1 formula (Davidon, 1959; Broyden, 1967), the DFP method (Davidon, 1959; Fletcher and Powell, 1963) and the BFGS method (Broyden, 1969; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970).”
Numerical Methods for Electronic Structure Calculations of Materials (2010, methodology): “In the 1960’s, Fletcher and Reeves generalized the conjugate gr dient algorithm to nonlinear problems [50] by building upon earlier work by Davidon [36] a nd Fletcher and Powell [49].”
Absolute comparison of simulated and experimental protein-folding dynamics (2002, unknown): “No memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton energy optimizatio”
Periodic solutions of the KdV equation (2010, methodology): “The resulting function of N variables was minimized using A. Jameson's version' of the Fletcher-Powell-Davidov algorithm [ 5 ].”
Inverse and Optimization Problems in Heat Transfer (2006, methodology): “For the Davidon-Fletcher-Powell (DFP) Method [33,34], such matrices are given by”