An efficient hybrid conjugate gradient-based projection method for convex constrained nonlinear monotone equations

2019 ◽  
Vol 22 (6) ◽  
pp. 1031-1050
Author(s):  
Mompati Koorapetse ◽  
P. Kaelo
Keyword(s):  
Projection Method ◽  
Conjugate Gradient ◽  
Monotone Equations ◽  
Gradient Based ◽  
Nonlinear Monotone Equations

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.

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 Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
San-Yang Liu ◽  
Yuan-Yuan Huang ◽  
Hong-Wei Jiao
Keyword(s):  
Global Convergence ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Monotone Equations ◽  
Mild Conditions ◽  
Sufficient Descent ◽  
Nonlinear Monotone Equations

Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.

scholarly journals An Accelerated Conjugate Gradient Algorithm for Solving Nonlinear Monotone Equations and Image Restoration Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Haishan Feng ◽  
Tingting Li
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient ◽  
Trust Region ◽  
Step Length ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Search Technique ◽  
Conjugate Gradient Algorithms ◽  
Monotone Equations ◽  
Nonlinear Monotone Equations

Combining the three-term conjugate gradient method of Yuan and Zhang and the acceleration step length of Andrei with the hyperplane projection method of Solodov and Svaiter, we propose an accelerated conjugate gradient algorithm for solving nonlinear monotone equations in this paper. The presented algorithm has the following properties: (i) All search directions generated by the algorithm satisfy the sufficient descent and trust region properties independent of the line search technique. (ii) A derivative-free search technique is proposed along the direction to obtain the step length αk. (iii) If ϕk=−αkhk−hwkTdk>0, then an acceleration scheme is used to modify the step length in a multiplicative manner and create a point. (iv) If the point satisfies the given condition, then it is the next point; otherwise, the hyperplane projection technique is used to obtain the next point. (v) The global convergence of the proposed algorithm is established under some suitable conditions. Numerical comparisons with other conjugate gradient algorithms show that the accelerated computing scheme is more competitive. In addition, the presented algorithm can also be applied to image restoration.

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