A sufficient descent Dai–Yuan type nonlinear conjugate gradient method for unconstrained optimization problems

2012 ◽  
Vol 72 (1-2) ◽  
pp. 101-112 ◽  
Author(s):  
Xian-zhen Jiang ◽  
Jin-bao Jian
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Nonlinear Conjugate Gradient Method ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent

scholarly journals A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 133 ◽  
Author(s):  
Xiuyun Zheng ◽  
Jiarong Shi
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Nonlinear Conjugate Gradient Method ◽  
Modified Method ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent

In this paper, a modification to the Polak–Ribiére–Polyak (PRP) nonlinear conjugate gradient method is presented. The proposed method always generates a sufficient descent direction independent of the accuracy of the line search and the convexity of the objective function. Under appropriate conditions, the modified method is proved to possess global convergence under the Wolfe or Armijo-type line search. Moreover, the proposed methodology is adopted in the Hestenes–Stiefel (HS) and Liu–Storey (LS) methods. Extensive preliminary numerical experiments are used to illustrate the efficiency of the proposed method.

scholarly journals Two Versions of the Spectral Nonlinear Conjugate Gradient Method

2018 ◽  
Vol 29 (1) ◽  
pp. 133
Author(s):  
Basim A. Hassan ◽  
Haneen A. Alashoor
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Convergence Properties ◽  
Nonlinear Conjugate Gradient Method ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

The nonlinear conjugate gradient method is widely used to solve unconstrained optimization problems. In this paper the development of different versions of nonlinear conjugate gradient methods with global convergence properties proved. Numerical results indicated that the proposed method is very efficient.

scholarly journals Global Convergence of a Nonlinear Conjugate Gradient Method

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Liu Jin-kui ◽  
Zou Li-min ◽  
Song Xiao-qian
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Nonlinear Conjugate Gradient Method ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Wolfe Line Search

A modified PRP nonlinear conjugate gradient method to solve unconstrained optimization problems is proposed. The important property of the proposed method is that the sufficient descent property is guaranteed independent of any line search. By the use of the Wolfe line search, the global convergence of the proposed method is established for nonconvex minimization. Numerical results show that the proposed method is effective and promising by comparing with the VPRP, CG-DESCENT, and DL+methods.

scholarly journals A Conjugate Gradient Method for Unconstrained Optimization Problems

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Gonglin Yuan
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Search Rule ◽  
Better Than

A hybrid method combining the FR conjugate gradient method and the WYL conjugate gradient method is proposed for unconstrained optimization problems. The presented method possesses the sufficient descent property under the strong Wolfe-Powell (SWP) line search rule relaxing the parameterσ<1. Under the suitable conditions, the global convergence with the SWP line search rule and the weak Wolfe-Powell (WWP) line search rule is established for nonconvex function. Numerical results show that this method is better than the FR method and the WYL method.

scholarly journals On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Min Sun ◽  
Jing Liu
Keyword(s):  
Strong Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Line Searches ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense thatlim infk→∞∥∇f(xk)∥=0when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense thatlimk→∞∥∇f(xk)∥=0under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.

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