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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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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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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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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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On the Behavior of Broyden’s Class of Quasi-Newton Methods
SIAM Journal on Optimization, 1992Summary: This paper analyzes algorithms from the Broyden class of quasi-Newton methods for nonlinear unconstrained optimization. This class depends on a parameter \(\phi_ k\), for which the choices \(\phi_ k=0\) and \(\phi_ k=1\) give the well-known BFGS and DFP methods.
Richard H. Byrd +2 more
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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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A quasi-Newton trust-region method
Mathematical Programming, 2004For nonlinear multivariate unconstrained optimization the quasi-Newton technique is used quite often, especially in those cases where the Hessian is either not known analytically or expensive to compute. E. Michael Gertz offers an approach which is based on the quasi-Newton method, but augmented with a line-search method to find a point that satisfies ...
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A quasi-Newton method with Cholesky factorization
Computing, 1980A quasi-Newton method for unconstrained minimization is presented, which uses a Cholesky factorization of an approximation to the Hessian matrix. In each step a new row and column of this approximation matrix is determined and its Cholesky factorization is updated. This reduces storage requirements and simplifies the calculation of the search direction.
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On the convergence of inexact quasi-newton methods
International Journal of Computer Mathematics, 1989This paper is concerned with quasi-Newton methods for solving systems of nonlinear equations, which make use of least-change secant updates. In the course of the iterative process, errors may be introduced and so the sequence actually computed differs from that produced in theory.
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