A Globally Convergent Derivative-Free Projection Method for Nonlinear Monotone Equations with Applications

2021 ◽  
Author(s):  
P. Kaelo ◽  
M. Koorapetse ◽  
C. R. Sam
Keyword(s):  
Projection Method ◽  
Monotone Equations ◽  
Globally Convergent ◽  
Derivative Free ◽  
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 THREE-TERM CONJUGATE GRADIENT-BASED PROJECTION METHOD FOR SOLVING LARGE-SCALE NONLINEAR MONOTONE EQUATIONS

2019 ◽  
Vol 24 (4) ◽  
pp. 550-563
Author(s):  
Mompati Koorapetse ◽  
Professor Kaelo
Keyword(s):  
Projection Method ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Sufficient Descent Condition ◽  
Monotone Equations ◽  
Derivative Free ◽  
Gradient Based ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Nonlinear Monotone Equations

A new three-term conjugate gradient-based projection method is presented in this paper for solving large-scale nonlinear monotone equations. This method is derivative-free and it is suitable for solving large-scale nonlinear monotone equations due to its lower storage requirements. The method satisfies the sufficient descent condition FTkdk ≤ −τ‖Fk‖2, where τ > 0 is a constant, and its global convergence is also established. Numerical results show that the method is efficient and promising.

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