scholarly journals A unified derivative-free projection method model for large-scale nonlinear equations with convex constraints

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yigui Ou ◽  
Wenjie Xu
Keyword(s):  
Nonlinear Equations ◽  
Projection Method ◽  
Large Scale ◽  
Practical Method ◽  
Projection Methods ◽  
Convex Constraints ◽  
Derivative Free ◽  
Constrained Equations ◽  
Practical Algorithm ◽  
Method Model

<p style='text-indent:20px;'>Motivated by recent derivative-free projection methods proposed in the literature for solving nonlinear constrained equations, in this paper we propose a unified derivative-free projection method model for large-scale nonlinear equations with convex constraints. Under mild conditions, the global convergence and convergence rate of the proposed method are established. In order to verify the feasibility and effectiveness of the model, a practical algorithm is devised and the corresponding numerical experiments are reported, which show that the proposed practical method is efficient and can be applied to solve large-scale nonsmooth equations. Moreover, the proposed practical algorithm is also extended to solve the obstacle problem.</p>

scholarly journals A New Conjugate Gradient Projection Method for Convex Constrained Nonlinear Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Pengjie Liu ◽  
Jinbao Jian ◽  
Xianzhen Jiang
Keyword(s):  
Nonlinear Equations ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Projection ◽  
Gradient Projection Method ◽  
Sparse Signals ◽  
Convex Constraints ◽  
Step Size ◽  
Constrained Nonlinear Equations

The conjugate gradient projection method is one of the most effective methods for solving large-scale monotone nonlinear equations with convex constraints. In this paper, a new conjugate parameter is designed to generate the search direction, and an adaptive line search strategy is improved to yield the step size, and then, a new conjugate gradient projection method is proposed for large-scale monotone nonlinear equations with convex constraints. Under mild conditions, the proposed method is proved to be globally convergent. A large number of numerical experiments for the presented method and its comparisons are executed, which indicates that the presented method is very promising. Finally, the proposed method is applied to deal with the recovery of sparse signals.

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 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.

scholarly journals A Derivative-Free Decent Method Via Acceleration Parameter for Solving Systems of Nonlinear Equations

2019 ◽  
Vol 2 (3) ◽  
pp. 1-4
Author(s):  
Abubakar Sani Halilu ◽  
M K Dauda ◽  
M Y Waziri ◽  
M Mamat
Keyword(s):  
Nonlinear Equations ◽  
Large Scale ◽  
Line Search ◽  
Main Idea ◽  
Step Length ◽  
Descent Method ◽  
Systems Of Nonlinear Equations ◽  
Inexact Line Search ◽  
Large Scale Systems ◽  
Derivative Free

An algorithm for solving large-scale systems of nonlinear equations based on the transformation of the Newton method with the line search into a derivative-free descent method is introduced. Main idea used in the algorithm construction is to approximate the Jacobian by an appropriate diagonal matrix. Furthermore, the step length is calculated using inexact line search procedure. Under appropriate conditions, the proposed method is proved to be globally convergent under mild conditions. The numerical results presented show the efficiency of the proposed method.

scholarly journals A method with inertial extrapolation step for convex constrained monotone equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdulkarim Hassan Ibrahim ◽  
Poom Kumam ◽  
Auwal Bala Abubakar ◽  
Jamilu Abubakar
Keyword(s):  
Global Convergence ◽  
Theoretical Analysis ◽  
Nonlinear Equations ◽  
Large Scale ◽  
Descent Direction ◽  
Monotone Equations ◽  
Derivative Free ◽  
Speed Up ◽  
Sufficient Descent ◽  
Inertial Extrapolation

AbstractIn recent times, various algorithms have been incorporated with the inertial extrapolation step to speed up the convergence of the sequence generated by these algorithms. As far as we know, very few results exist regarding algorithms of the inertial derivative-free projection method for solving convex constrained monotone nonlinear equations. In this article, the convergence analysis of a derivative-free iterative algorithm (Liu and Feng in Numer. Algorithms 82(1):245–262, 2019) with an inertial extrapolation step for solving large scale convex constrained monotone nonlinear equations is studied. The proposed method generates a sufficient descent direction at each iteration. Under some mild assumptions, the global convergence of the sequence generated by the proposed method is established. Furthermore, some experimental results are presented to support the theoretical analysis of the proposed method.

Spectral gradient projection method for monotone nonlinear equations with convex constraints

2009 ◽  
Vol 59 (10) ◽  
pp. 2416-2423 ◽  
Author(s):  
Zhensheng Yu ◽  
Ji Lin ◽  
Jing Sun ◽  
Yunhai Xiao ◽  
Liying Liu ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Projection Method ◽  
Gradient Projection ◽  
Gradient Projection Method ◽  
Convex Constraints
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