scholarly journals Smoothing Nonlinear Conjugate Gradient Method for Image Restoration Using Nonsmooth Nonconvex Minimization

2010 ◽  
Vol 3 (4) ◽  
pp. 765-790 ◽  
Author(s):  
Xiaojun Chen ◽  
Weijun Zhou
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Nonconvex Minimization ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient

scholarly journals A Modified Nonlinear Conjugate Gradient Method with the Armijo Line Search and Its Application

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Mengxiang Zhang ◽  
Yingjie Zhou ◽  
Songhua Wang
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Gradient Methods ◽  
Linear Convergence ◽  
Nonlinear Conjugate Gradient Method ◽  
Armijo Line Search ◽  
Nonlinear Conjugate Gradient

In this article, a modified Polak-Ribière-Polyak (PRP) conjugate gradient method is proposed for image restoration. The presented method can generate sufficient descent directions without any line search conditions. Under some mild conditions, this method is globally convergent with the Armijo line search. Moreover, the linear convergence rate of the modified PRP method is established. The experimental results of unconstrained optimization, image restoration, and compressive sensing show that the proposed method is promising and competitive with other conjugate gradient methods.

scholarly journals A Modified Conjugacy Condition and Related Nonlinear Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shengwei Yao ◽  
Xiwen Lu ◽  
Bin Qin
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Special Role ◽  
Conjugacy Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
The Given

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. In this paper, we propose a new conjugacy condition which is similar to Dai-Liao (2001). Based on this condition, the related nonlinear conjugate gradient method is given. With some mild conditions, the given method is globally convergent under the strong Wolfe-Powell line search for general functions. The numerical experiments show that the proposed method is very robust and efficient.

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