Results 261 to 270 of about 124,946 (301)
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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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A Classification of Quasi-Newton Methods
Numerical Algorithms, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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Quasi- Newton Methods for Nonlinear Equations
Journal of the ACM, 1968A unified derivation is presented of the quasi-Newton methods for solving systems of nonlinear equations. The general algorithm contains, as special cases, all of the previously proposed quasi-Newton methods.
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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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Maximum Entropy Derivation of Quasi-Newton Methods
SIAM Journal on Optimization, 2016Summary: This paper presents a maximum-entropy (MaxEnt) derivation of many commonly used quasi-Newton rules. (i) This derivation interprets the elements of the Jacobian or Hessian as means of a multivariate probability distribution; (ii) the variance is chosen to represent the uncertainty about the mean.
Steven H. Waldrip, Robert K. Niven
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Cancellation Errors in Quasi-Newton Methods
SIAM Journal on Scientific and Statistical Computing, 1986Using a probabilistic estimate, the author gives the effect of cancellation on the performance of quasi-Newton methods. First, the author describes and shows that the size of the low rank correction can be measured for the BFGS method. This BFGS method is used to find a local solution \(x^*\) of the problem: minimize f(x), \(x\in {\mathbb{R}}^ n ...
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Optimization of Simulation via Quasi-Newton Methods
ORSA Journal on Computing, 1994This paper discusses the application of quasi-Newton methods to optimization of simulation. Specifically, it describes a general methodology that combines response surface methodology and other optimization techniques with quasi-Newton methods. Using quasi-Newton methods in the vicinity of the optimum speeds up the convergence rate of response surface
M. Hossein Safizadeh, Robert Signorile
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