A New Hybrid PRP-DY Conjugate Gradient Method

Dong, Junli; Jiao, Baocong; Chen, Lanping

doi:10.1109/cso.2010.27

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…a) The level set 𝜉 = {𝑥𝜖𝑅 𝑛 |𝑓(𝑥) ≤ 𝑓(𝑥 1 } is bounded. b) f(x) is continuously differentiable and its gradient is Lipchitz continuous in some neighborhood u of 𝜉, that is to say in particular, there exists a constant 𝑝 > 0 such that ‖𝑔(𝑥) − 𝑔(𝑦)‖ ≤ ‖𝑥 − 𝑦‖ ∀ 𝑥, 𝑦𝜖𝜉 , more details can be found in [17], The well-known Zoutendijk condition [18] is given by the following lemma.…”

Section: Global Convergencementioning

confidence: 99%

A new conjugate gradient algorithms using conjugacy condition for solving unconstrained optimization

Qasim

Salih

Hassan

2021

IJEECS

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The primarily objective of this paper which is indicated in the field of conjugate gradient algorithms for unconstrained optimization problems and algorithms is to show the advantage of the new proposed algorithm in comparison with the standard method which is denoted as. Hestenes Stiefel method, as we know the coefficient conjugate parameter is very crucial for this reason, we proposed a simple modification of the coefficient conjugate gradient which is used to derived the new formula for the conjugate gradient update parameter described in this paper. Our new modification is based on the conjugacy situation for nonlinear conjugate gradient methods which is given by the conjugacy condition for nonlinear conjugate gradient methods and added a nonnegative parameter to suggest the new extension of the method. Under mild Wolfe conditions, the global convergence theorem and lemmas are also defined and proved. The proposed method's efficiency is programming and demonstrated by the numerical instances, which were very encouraging.

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Section: Global Convergencementioning

confidence: 99%

A new conjugate gradient algorithms using conjugacy condition for solving unconstrained optimization

Qasim

Salih

Hassan

2021

IJEECS

View full text Add to dashboard Cite

show abstract

“…Dai and Yuan [20] proposed a CG method for unconstrained optimization and proved the global convergence of these hybrid computational schemes. Dong and Jiao [21] proposed a convex combination of the PRP and DY methods for solving nonlinear equations. Furthermore, the projection technique proposed by Solodov and Svaiter [22] motivated many scholars to further develop methods for solving (1) [23,24].…”

Section: Introductionmentioning

confidence: 99%

A New Hybrid PRPFR Conjugate Gradient Method for Solving Nonlinear Monotone Equations and Image Restoration Problems

Zhou

2020

Mathematical Problems in Engineering

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A new hybrid PRPFR conjugate gradient method is presented in this paper, which is designed such that it owns sufficient descent property and trust region property. This method can be considered as a convex combination of the PRP method and the FR method while using the hyperplane projection technique. Under accelerated step length, the global convergence property is gained with some appropriate assumptions. Comparing with other methods, the numerical experiments show that the PRPFR method is more competitive for solving nonlinear equations and image restoration problems.

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Prediction of Cutting Concentration in Horizontal wells for Different well Inclination Sections

Zhang,

Cai,

Wei

et al. 2023

Chem Technol Fuels Oils

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A New Hybrid PRP-DY Conjugate Gradient Method

Cited by 3 publications

References 13 publications

A new conjugate gradient algorithms using conjugacy condition for solving unconstrained optimization

A new conjugate gradient algorithms using conjugacy condition for solving unconstrained optimization

A New Hybrid PRPFR Conjugate Gradient Method for Solving Nonlinear Monotone Equations and Image Restoration Problems

Prediction of Cutting Concentration in Horizontal wells for Different well Inclination Sections

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