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Stochastic Quasi-Newton Methods
Proceedings of the IEEE, 2020Large-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, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chengxian Xu, Jianzhong Zhang 0001
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Approximate quasi-Newton methods
Mathematical Programming, 1990Newton-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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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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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 for implicit black-box FSI coupling [PDF]
Computer Methods in Applied Mechanics and Engineering, 2014 In this paper we introduce a new multi-vector update quasi-Newton (MVQN) method for implicit coupling of partitioned, transient FSI solvers. The new quasi-Newton method facilitates the use of ‘black-box’ field solvers and under certain circumstances ...
A E J Bogaers, Schalk Kok, B D Reddy
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A Classification of Quasi-Newton Methods
Numerical Algorithms, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A comparison of the Gauss–Newton and quasi-Newton methods in resistivity imaging inversion [PDF]
Journal of Applied Geophysics, 2002 The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets.
M H Loke, T Dahlin
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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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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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Relaxation of Crystals with the Quasi-Newton Method
Journal of Computational Physics, 1997The authors present a relaxation scheme for crystals with the quasi-Newton method. The method preserves the crystal structure during relaxation. The efficiency of the method is demonstrated for silicon test problems.
Pfrommer, Bernd G. +3 more
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2019
The Quasi-Newton methods do not compute the Hessian of nonlinear functions. The Hessian is updated by analyzing successive gradient vectors instead. The Quasi-Newton algorithm was first proposed by William C. Davidon, a physicist while working at Argonne National Laboratory, United States in 1959.
Shashi Kant Mishra, Bhagwat Ram
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The Quasi-Newton methods do not compute the Hessian of nonlinear functions. The Hessian is updated by analyzing successive gradient vectors instead. The Quasi-Newton algorithm was first proposed by William C. Davidon, a physicist while working at Argonne National Laboratory, United States in 1959.
Shashi Kant Mishra, Bhagwat Ram
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