A globally convergent version of the Polak-Ribière conjugate gradient method

1997 ◽  
Vol 78 (3) ◽  
pp. 375-391 ◽  
Author(s):  
L. Grippo ◽  
S. Lucidi
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Globally Convergent

Truss Structural Optimization Based on Globally Convergent Version of MMA

2013 ◽  
Vol 694-697 ◽  
pp. 2783-2786
Author(s):  
Li Hua Guo ◽  
Wen Cheng Tang
Keyword(s):  
Structural Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimal Solution ◽  
Unconstrained Minimization ◽  
Dual Method ◽  
Globally Convergent

The subproblem of the globally convergent version of method of moving asymptotes (GCMMA) was deeply studied and realized by Lagrange dual method, sequential unconstrained minimization technique (SUMT) and conjugate gradient method. Based on the convex, separable and conservative properties of subproblem, a dual problem was built by using Lagrange dual method. The dual problem was transformed into unconstrained optimization problem using SUMT and solved by conjugate gradient method. Finally, the feasibility of solution of subproblem is demonstrated by truss structural optimization problem. Comparing with other optimization algorithms, GCMMA can converge to the global optimal solution.

scholarly journals A Globally Convergent Hybrid Conjugate Gradient Method and Its Numerical Behaviors

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Yuan-Yuan Huang ◽  
San-Yang Liu ◽  
Xue-Wu Du ◽  
Xiao-Liang Dong
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Globally Convergent ◽  
Numerical Performance ◽  
Hybrid Conjugate Gradient Method

We consider a hybrid Dai-Yuan conjugate gradient method. We confirm that its numerical performance can be improved provided that this method uses a practical steplength rule developed by Dong, and the associated convergence is analyzed as well.

scholarly journals A Modified Conjugate Gradient Method for Solving Large-Scale Nonlinear Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Hongbo Guan ◽  
Sheng Wang
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Experiments ◽  
Large Scale ◽  
Globally Convergent ◽  
Weaker Conditions ◽  
Modified Conjugate Gradient Method

In this paper, we propose a modified Polak–Ribière–Polyak (PRP) conjugate gradient method for solving large-scale nonlinear equations. Under weaker conditions, we show that the proposed method is globally convergent. We also carry out some numerical experiments to test the proposed method. The results show that the proposed method is efficient and stable.

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