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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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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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A quasi-Newton method for non-smooth equations
International Journal of Computer Mathematics, 2005We introduce a quasi-Newton method for non-smooth equations. The proposed method is convergent and its convergence is q-superlinear. Some computational results are presented.
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Quasi-Newton methods for saddlepoints
Journal of Optimization Theory and Applications, 1985The well-known quadratically convergent methods of the Huang type [cf. \textit{H. Y. Huang}, ibid. 5, 405-423 (1970; Zbl 0184.202) and \textit{H. Y. Huang} and \textit{A. V. Levy}, ibid. 6, 269-282 (1970; Zbl 0187.404)] to maximize or minimize a function \(f: {\mathbb{R}}^ n\to {\mathbb{R}}\) are generalized to find saddlepoints of f.
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A family of the quasi-Newton methods
TRU Mathematics, 1980YAMAKI, NAOKAZU, YABE, HIROSHI
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A Newton-type method for quasi-equilibrium problems and applications
Optimization, 2022Pedro Jorge S Santos, P S M Santos
exaly