Use of a nonquadratic model in a conjugate-gradient method of optimization with inexact line searches

1984 ◽  
Vol 43 (3) ◽  
pp. 357-370 ◽  
Author(s):  
A. Tassopoulos ◽  
C. Storey
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Searches ◽  
Inexact Line Searches

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.

scholarly journals A NEW THREE–TERM CONJUGATE GRADIENT METHOD WITH DESCENT DIRECTION FOR UNCONSTRAINED OPTIMIZATION

2016 ◽  
Vol 21 (3) ◽  
pp. 399-411 ◽  
Author(s):  
XiaoLiang Dong ◽  
HongWei Liu ◽  
YuBo He ◽  
Saman Babaie-Kafaki ◽  
Reza Ghanbari
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Numerical Comparison ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Line Searches ◽  
Sufficient Descent ◽  
Descent Condition

In this paper, we propose a three–term PRP–type conjugate gradient method which always satisfies the sufficient descent condition independently of line searches employed. An important property of our method is that its direction is closest to the direction of the Newton method or satisfies conjugacy condition as the iterations evolve. In addition, under mild condition, we prove global convergence properties of the proposed method. Numerical comparison illustrates that our proposed method is efficient for solving the optimization problems.

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