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A FAMILY OF THE QUASI-NEWTON METHODS

open access: yesA FAMILY OF THE QUASI-NEWTON METHODS
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Stochastic Quasi-Newton Methods

Proceedings of the IEEE, 2020
Large-scale data science trains models for data sets containing massive numbers of samples. Training is often formulated as the solution of empirical risk minimization problems that are optimization programs whose complexity scales with the number of elements in the data set.
Aryan Mokhtari, Alejandro Ribeiro
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A Survey of Quasi-Newton Equations and Quasi-Newton Methods for Optimization

Annals of Operations Research, 2001
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Chengxian Xu, Jianzhong Zhang 0001
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Approximate quasi-Newton methods

Mathematical Programming, 1990
Newton-like iterative methods for nonlinear equations on Banach spaces are considered. It is proved how the local convergence behaviour of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are included.
C. T. Kelley, Ekkehard W. Sachs
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Quasi-Newton Methods

2021
In Chap. 6, multidimensional optimization methods were considered in which the search for the minimizer is carried out by using a set of conjugate directions. An important feature of some of these methods (e.g., the Fletcher–Reeves and Powell’s methods) is that explicit expressions for the second derivatives of \(f(\mathbf{x})\) are not required ...
Andreas Antoniou, Wu-Sheng Lu
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Quasi-Newton Methods

2008
In this chapter we take another approach toward the development of methods lying somewhere intermediate to steepest descent and Newton’s method. Again working under the assumption that evaluation and use of the Hessian matrix is impractical or costly, the idea underlying quasi-Newton methods is to use an approximation to the inverse Hessian in place of
David G. Luenberger, Yinyu Ye
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A Classification of Quasi-Newton Methods

Numerical Algorithms, 2003
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