A self-adaptive three-term conjugate gradient method for monotone nonlinear equations with convex constraints

CALCOLO ◽  
2015 ◽  
Vol 53 (2) ◽  
pp. 133-145 ◽  
Author(s):  
X. Y. Wang ◽  
S. J. Li ◽  
X. P. Kou
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Constraints ◽  
Self Adaptive

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 AN EFFICIENT HYBRID DERIVATIVE-FREE PROJECTION ALGORITHM FOR CONSTRAINT NONLINEAR EQUATIONS

2021 ◽  
Vol 40 (3) ◽  
pp. 64-75
Author(s):  
Kanikar Muangchoo
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Projection Algorithm ◽  
Monotonicity Condition ◽  
Convex Constraints ◽  
Sufficient Descent Condition ◽  
Lipschitz Continuous ◽  
Derivative Free

In this paper, by combining the Solodov and Svaiter projection technique with the conjugate gradient method for unconstrained optimization proposed by Mohamed et al. (2020), we develop a derivative-free conjugate gradient method to solve nonlinear equations with convex constraints. The proposed method involves a spectral parameter which satisfies the sufficient descent condition. The global convergence is proved under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Numerical experiment shows that the proposed method is efficient.

scholarly journals Spectral CG Algorithm for Solving Fuzzy Nonlinear Equations

2022 ◽  
pp. 1-10
Author(s):  
Mezher M. Abed ◽  
Ufuk Öztürk ◽  
Hisham M. Khudhur
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Conjugacy Condition ◽  
Wide Range ◽  
Non Linear ◽  
Fuzzy Equations

The nonlinear conjugate gradient method is an effective technique for solving large-scale minimizations problems, and has a wide range of applications in various fields, such as mathematics, chemistry, physics, engineering and medicine. This study presents a novel spectral conjugate gradient algorithm (non-linear conjugate gradient algorithm), which is derived based on the Hisham–Khalil (KH) and Newton algorithms. Based on pure conjugacy condition The importance of this research lies in finding an appropriate method to solve all types of linear and non-linear fuzzy equations because the Buckley and Qu method is ineffective in solving fuzzy equations. Moreover, the conjugate gradient method does not need a Hessian matrix (second partial derivatives of functions) in the solution. The descent property of the proposed method is shown provided that the step size at meets the strong Wolfe conditions. In numerous circumstances, numerical results demonstrate that the proposed technique is more efficient than the Fletcher–Reeves and KH algorithms in solving fuzzy nonlinear equations.

Motion control of the two joint planar robotic manipulators through accelerated Dai–Liao method for solving system of nonlinear equations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abubakar Sani Halilu ◽  
Arunava Majumder ◽  
Mohammed Yusuf Waziri ◽  
Kabiru Ahmed ◽  
Aliyu Muhammed Awwal
Keyword(s):  
Motion Control ◽  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Robotic Manipulators ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Content Type ◽  
Conjugate Gradient Algorithms

PurposeThe purpose of this research is to propose a new choice of nonnegative parameter t in Dai–Liao conjugate gradient method.Design/methodology/approachConjugate gradient algorithms are used to solve both constrained monotone and general systems of nonlinear equations. This is made possible by combining the conjugate gradient method with the Newton method approach via acceleration parameter in order to present a derivative-free method.FindingsA conjugate gradient method is presented by proposing a new Dai–Liao nonnegative parameter. Furthermore the proposed method is successfully applied to handle the application in motion control of the two joint planar robotic manipulators.Originality/valueThe proposed algorithm is a new approach that will not either submitted or publish somewhere.

A RECENT MODIFICATION ON DAI-LIAO CONJUGATE GRADIENT METHOD FOR SOLVING SYMMETRIC NONLINEAR EQUATIONS

2018 ◽  
Vol 103 (12) ◽  
pp. 1961-1974
Author(s):  
Usman Abbas Yakubu ◽  
Mustafa Mamat ◽  
Mohamad Afendee Mohamad ◽  
Mohd Rivaie ◽  
Jamilu Sabi’u
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Recent Modification
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