A derivative-free iterative method for nonlinear monotone equations with convex constraints

2018 ◽  
Vol 82 (1) ◽  
pp. 245-262 ◽  
Author(s):  
Jinkui Liu ◽  
Yuming Feng
Keyword(s):  
Iterative Method ◽  
Convex Constraints ◽  
Monotone Equations ◽  
Derivative Free ◽  
Nonlinear Monotone Equations

A descent derivative-free algorithm for nonlinear monotone equations with convex constraints

2020 ◽  
Vol 54 (2) ◽  
pp. 489-505 ◽  
Author(s):  
Hassan Mohammad ◽  
Auwal Bala Abubakar
Keyword(s):  
Numerical Experiments ◽  
Line Search ◽  
Iteration Step ◽  
Descent Direction ◽  
Positive Parameter ◽  
Convex Constraints ◽  
Residual Vector ◽  
Monotone Equations ◽  
Derivative Free ◽  
Nonlinear Monotone Equations

In this paper, we present a derivative-free algorithm for nonlinear monotone equations with convex constraints. The search direction is a product of a positive parameter and the negation of a residual vector. At each iteration step, the algorithm generates a descent direction independent from the line search used. Under appropriate assumptions, the global convergence of the algorithm is given. Numerical experiments show the algorithm has advantages over the recently proposed algorithms by Gao and He (Calcolo 55 (2018) 53) and Liu and Li (Comput. Math. App. 70 (2015) 2442–2453).

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.

Accelerated derivative‐free method for nonlinear monotone equations with an application

2021 ◽  
Author(s):  
Abdulkarim Hassan Ibrahim ◽  
Poom Kumam ◽  
Auwal Bala Abubakar ◽  
Abubakar Adamu
Keyword(s):  
Monotone Equations ◽  
Derivative Free ◽  
Derivative Free Method ◽  
Nonlinear Monotone Equations

scholarly journals Derivative-free method based on DFP updating formula for solving convex constrained nonlinear monotone equations and application

2021 ◽  
Vol 6 (8) ◽  
pp. 8792-8814
Author(s):  
Aliyu Muhammed Awwal ◽  
◽  
Poom Kumam ◽  
Kanokwan Sitthithakerngkiet ◽  
Abubakar Muhammad Bakoji ◽  
...  
Keyword(s):  
Monotone Equations ◽  
Derivative Free ◽  
Derivative Free Method ◽  
Nonlinear Monotone Equations

scholarly journals A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 168 ◽  
Author(s):  
Zhifeng Dai ◽  
Huan Zhu
Keyword(s):  
Global Convergence ◽  
Large Scale ◽  
Line Search ◽  
System Of Nonlinear Equations ◽  
Inexact Newton Method ◽  
Monotone Equations ◽  
Smoothing Methods ◽  
Derivative Free ◽  
Derivative Free Method ◽  
Nonlinear Monotone Equations

The goal of this paper is to extend the modified Hestenes-Stiefel method to solve large-scale nonlinear monotone equations. The method is presented by combining the hyperplane projection method (Solodov, M.V.; Svaiter, B.F. A globally convergent inexact Newton method for systems of monotone equations, in: M. Fukushima, L. Qi (Eds.)Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Academic Publishers. 1998, 355-369) and the modified Hestenes-Stiefel method in Dai and Wen (Dai, Z.; Wen, F. Global convergence of a modified Hestenes-Stiefel nonlinear conjugate gradient method with Armijo line search. Numer Algor. 2012, 59, 79-93). In addition, we propose a new line search for the derivative-free method. Global convergence of the proposed method is established if the system of nonlinear equations are Lipschitz continuous and monotone. Preliminary numerical results are given to test the effectiveness of the proposed method.

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