An increasing-angle property of the conjugate gradient method and the implementation of large-scale minimization algorithms with line searches

2002 ◽  
Vol 10 (4) ◽  
pp. 323-334
Author(s):  
Yu-Hong Dai ◽  
José Mario Martínez ◽  
Jin-Yun Yuan
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Searches ◽  
Minimization Algorithms ◽  
Angle Property

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.

Large-Scale Parallel Finite Element Analysis of the Stress Singular Problems

2002 ◽  
Author(s):  
Noriyuki Kushida ◽  
Hiroshi Okuda ◽  
Genki Yagawa
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Preconditioned Conjugate Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Singular Problems ◽  
Parallel Finite Element

In this paper, the convergence behavior of large-scale parallel finite element method for the stress singular problems was investigated. The convergence behavior of iterative solvers depends on the efficiency of the preconditioners. However, efficiency of preconditioners may be influenced by the domain decomposition that is necessary for parallel FEM. In this study the following results were obtained: Conjugate gradient method without preconditioning and the diagonal scaling preconditioned conjugate gradient method were not influenced by the domain decomposition as expected. symmetric successive over relaxation method preconditioned conjugate gradient method converged 6% faster as maximum if the stress singular area was contained in one sub-domain.

Application of Jacobi - Conjugate Gradient Method in the Two-Dimensional Magnetotelluric Forward

2013 ◽  
Vol 416-417 ◽  
pp. 2123-2127
Author(s):  
Chong Li Zhu
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Linear Equations ◽  
Hessian Matrix ◽  
Simulation Method ◽  
Coefficient Matrix ◽  
Fine Grid ◽  
Solution Efficiency

Using the finite element method and all kinds of numerical simulation method, A large-scale system of linear equations is solved eventually,the solution method of the system of equations largely determines the solution efficiency and precision of numerical calculation. The Jacobi iteration preconditioning conjugate gradient method is adopted, Both overcome the coefficient matrix pathological characteristics and the characteristics of slow convergence speed ,and avoid the disadvantages such as Newton's method to store and Hessian matrix is calculated and inversed,improve forward modeling calculation speed and accuracy. Guarantee for solving numerical stability and efficiency ,of the thick grid combined with verification, the algorithm is feasible and it is verified by coarse grid combine with fine grid.

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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