Practical Methods of Optimization: Fletcher/Practical Methods of Optimization

By Roger Fletcher. 2000

10,471 citations recorded by the source corpus.

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In Numerical Analysis

Citations in the corpus

Balanced Policy Evaluation and Learning (2017, methodology): “We focus on p = 2 for brevity. where t � T i t � T j t K t ( X i , X j ) + 2⇤ , and To leverage this result, we use a parameterized policy class such as ⇧ logit = { ⇡ t ( x ; t ) / exp( t 0 + Tt x ) (or kernelized versions thereof), apply chain rule to diﬀerentiate objective in the parameters � , an”
New Insights and Perspectives on the Natural Gradient Method (2014, methodology): “A survey of such methods is outside the scope of this report, but many good references and reviews are available (e.g. Nocedal and Wright, 2006; Fletcher, 2013).”
Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey (2018, methodology): “Previously, Lyu et al. [28] also used the notion of penalizing the gradient of loss function of network models with respect to the inputs to incorporate robustness in the networks against L-BFGS [22] and FGSM [23] based attacks.”
Kernel methods in machine learning (2007, neutral): “Equation (51) is a quadratic program which can be solved efficiently (Fletcher [51]).”
Artificial neural networks for solving ordinary and partial differential equations (1997, methodology): “From the several algorithms that are implemented therein, the quasi-Newton BFGS [ 9 ] method seemed to perform better in these problems and hence we used it in all of our experiments.”
Shampoo: Preconditioned Stochastic Tensor Optimization (2018, methodology): “Classic algorithms in this family include Newton’s method, which employs the local Hessian as a preconditioner, as well as a plethora of quasi-Newton methods (e.g., [8, 15, 19]) that can be used whenever second-order information is unavailable or too expensive to compute.”
3‐D magnetic inversion with data compression and image focusing (2002, methodology): “The solution of compressed inverse problem (5) is found iteratively according to the following formulas (Fletcher, 1981):”
Antenna Current Optimization using MATLAB and CVX (2016, methodology): “There are also many efficient solvers for convex optimization problems and these solvers can provide error estimates [6, 19].”
Weighted Low-Rank Approximation of General Complex Matrices and Its Application in the Design of 2-D Digital Filters (1997, background): “[18] G.”
Parameter estimation from load-sharing system data using the expectation–maximization algorithm (2013, methodology): “For specific details on the BFGS method, the reader is referred to Fletcher (2000).”
Nonlinear optimization and support vector machines (2018, methodology): “We address the reader to [2], [54], [20] for insights on the duality in nonlinear programming.”
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs (2020, methodology): “We will follow standard practice in machine learning and solving this minimization problem approximately by either (first-order) stochastic gradient descent methods such as ADAM [30] or even higher-order optimization methods such as different variants of the LBFGS algorithm [20].”