An efficient three-term conjugate gradient method for nonlinear monotone equations with convex constraints

CALCOLO ◽  
2018 ◽  
Vol 55 (4) ◽  
Author(s):  
Peiting Gao ◽  
Chuanjiang He
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Constraints ◽  
Monotone Equations ◽  
Nonlinear Monotone Equations

scholarly journals A modified Perry-type derivative-free projection method for solving large-scale nonlinear monotone equations

2021 ◽  
Author(s):  
Mompati Koorapetse ◽  
P Kaelo ◽  
S Kooepile-Reikeletseng
Keyword(s):  
Global Convergence ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Numerical Results ◽  
Projection Technique ◽  
Monotone Equations ◽  
Derivative Free ◽  
Nonlinear Monotone Equations

In this paper, a new modified Perry-type derivative-free projection method for solving large-scale nonlinear monotone equations is presented. The method is developed by combining a modified Perry's conjugate gradient method with the hyperplane projection technique. Global convergence and numerical results of the proposed method are established. Preliminary numerical results show that the proposed method is promising and efficient compared to some existing methods in the literature.

scholarly journals A New Hybrid PRPFR Conjugate Gradient Method for Solving Nonlinear Monotone Equations and Image Restoration Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yingjie Zhou ◽  
Yulun Wu ◽  
Xiangrong Li
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Combination ◽  
Trust Region ◽  
Step Length ◽  
Monotone Equations ◽  
Global Convergence Property ◽  
Sufficient Descent

A new hybrid PRPFR conjugate gradient method is presented in this paper, which is designed such that it owns sufficient descent property and trust region property. This method can be considered as a convex combination of the PRP method and the FR method while using the hyperplane projection technique. Under accelerated step length, the global convergence property is gained with some appropriate assumptions. Comparing with other methods, the numerical experiments show that the PRPFR method is more competitive for solving nonlinear equations and image restoration problems.

scholarly journals A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sheng Wang ◽  
Hongbo Guan
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Convex Constraints ◽  
Type Method ◽  
Scaled Conjugate Gradient ◽  
Unconstrained Optimization Problems

Based on the Scaled conjugate gradient (SCALCG) method presented by Andrei (2007) and the projection method presented by Solodov and Svaiter, we propose a SCALCG method for solving monotone nonlinear equations with convex constraints. SCALCG method can be regarded as a combination of conjugate gradient method and Newton-type method for solving unconstrained optimization problems. So, it has the advantages of the both methods. It is suitable for solving large-scale problems. So, it can be applied to solving large-scale monotone nonlinear equations with convex constraints. Under reasonable conditions, we prove its global convergence. We also do some numerical experiments show that the proposed method is efficient and promising.

Sign in / Sign up

Export Citation Format

Share Document