Results 291 to 300 of about 76,549 (323)

Two modified Dai-Yuan nonlinear conjugate gradient methods

Numerical Algorithms, 2008
The author improves the iterative method \[ x_{k+1}=x_k+\alpha_k d_k;\;d_0=-g_k,\;d_k=-g_k+\beta_k d_{k-1},\;k>0;\;g(x)=f^{\prime}(x),\;g_k=g(x_k) \] for solving smooth unconstrained optimization problems \(\min_{x \in\mathbb R^n} f(x)\). In the original version of the method, \[ \beta_k=\| g_k \|^2/d^T_{k-1}y_{k-1},\;y_{k-1}=g_k-g_{k-1}, \] and the ...
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A spectral conjugate gradient method for nonlinear inverse problems

Inverse Problems in Science and Engineering, 2017
AbstractIn this study, a new spectral conjugate gradient method is presented to solve nonlinear inverse problems, which transferred into the unconstrained nonlinear optimization with a neighbour term. The global convergence and regularizing properties of the proposed method are analysed.
Zhibin Zhu, Huajun Wang, Benxin Zhang
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A Class of Descent Nonlinear Conjugate Gradient Methods

2013 Fourth International Conference on Digital Manufacturing & Automation, 2013
This thesis further study descent conjugate gradient methods based on the modified FR method and the modified PRP method give the class of conjugate gradient methods formed by the convex combination of the MFR method and the MPRP method. This class of methods enjoys the same nice properties as those of the MFR method and the MPRP method.
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Conjugate gradient methods for linearly constrained nonlinear programming

1982
This paper considers the problem of minimizing a nonlinear function subject to linear constraints. The method adopted is the reduced gradient method as described by Murtagh and Saunders, with a conjugate gradient method due to Shanno used for unconstrained minimization on manifolds. It is shown how to preserve past information on search directions when
Shanno, D. F., Marsten, R. E.
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Sufficient descent nonlinear conjugate gradient methods with conjugacy condition

Numerical Algorithms, 2009
The authors consider unconstrained optimization problems with a continuously differentiable objective function \(f: \mathbb{R}^n\to\mathbb{R}\). A class of modified conjugate gradient methods is proposed for solving the problems. The methods in this class have a common property that the direction \(d_k\) generated at iteration \(k\) and corresponding ...
Cheng, Wanyou, Liu, Qunfeng
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Conjugate-Gradient Methods for Large-Scale Nonlinear Optimization.

1979
Abstract : In this paper we discuss several recent conjugate-gradient type methods for solving large-scale nonlinear optimization problems. We demonstrate how the performance of these methods can be significantly improved by careful implementation. A method based upon iterative preconditioning will be suggested which performs reasonably efficiently on ...
Walter Murray, Philip E. Gill
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AN ADAPTIVE CONJUGACY CONDITION AND RELATED NONLINEAR CONJUGATE GRADIENT METHODS

International Journal of Computational Methods, 2014
In an attempt to find a reasonable solution for an open problem propounded by Andrei in nonlinear conjugate gradient methods, an adaptive conjugacy condition is proposed. The suggested condition is designed based on an implicit switch from a conjugacy condition to the standard secant equation, using an extended conjugacy condition proposed by Dai and ...
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A scaled conjugate gradient method for nonlinear unconstrained optimization

Optimization Methods and Software, 2016
We propose a new optimization problem which combines the good features of the classical conjugate gradient method using some penalty parameter, and then, solve it to introduce a new scaled conjugate gradient method for solving unconstrained problems. The method reduces to the classical conjugate gradient algorithm under common assumptions, and inherits
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Magnetic resonance linear accelerator technology and adaptive radiation therapy: An overview for clinicians

Ca-A Cancer Journal for Clinicians, 2022
William A Hal, X Allen Li, Daniel A Low
exaly  

Advances in nonlinear conjugate gradient methods

SCIENTIA SINICA Mathematica
Dai Yu-Hong, Liu Zexian
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