Some three-term conjugate gradient methods with the new direction structure

Liu, J.K.; Zhao, Yongxiang; Wu, Xiaoyu

doi:10.1016/j.apnum.2019.10.011

Cited by 18 publications

(2 citation statements)

References 30 publications

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“…Liu et al [17] demonstrated how nonconvex functions may address nonlinear monotone equations if the sufficient descent condition is met. Meanwhile, Liu et al [18] created the three-term CG methods given below and solved Equation (1) by utilizing it in order to avoid using the condition (…”

Section: Introductionmentioning

confidence: 99%

A three-term conjugate gradient descent method with some applications

Alhawarat,

Salleh,

Alolaiyan

et al. 2024

J Inequal Appl

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The stationary point of optimization problems can be obtained via conjugate gradient (CG) methods without the second derivative. Many researchers have used this method to solve applications in various fields, such as neural networks and image restoration. In this study, we construct a three-term CG method that fulfills convergence analysis and a descent property. Next, in the second term, we employ a Hestenses-Stiefel CG formula with some restrictions to be positive. The third term includes a negative gradient used as a search direction multiplied by an accelerating expression. We also provide some numerical results collected using a strong Wolfe line search with different sigma values over 166 optimization functions from the CUTEr library. The result shows the proposed approach is far more efficient than alternative prevalent CG methods regarding central processing unit (CPU) time, number of iterations, number of function evaluations, and gradient evaluations. Moreover, we present some applications for the proposed three-term search direction in image restoration, and we compare the results with well-known CG methods with respect to the number of iterations, CPU time, as well as root-mean-square error (RMSE). Finally, we present three applications in regression analysis, image restoration, and electrical engineering.

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Section: Introductionmentioning

confidence: 99%

A three-term conjugate gradient descent method with some applications

Alhawarat,

Salleh,

Alolaiyan

et al. 2024

J Inequal Appl

View full text Add to dashboard Cite

show abstract

“…and they used it to solve equation (1). Liu et al [24] proposed wide choices using equation ( 21) as follows:…”

Section: Introductionmentioning

confidence: 99%

A Descent Four-Term Conjugate Gradient Method with Global Convergence Properties for Large-Scale Unconstrained Optimisation Problems

Alhawarat

Alhamzi

Masmali

et al. 2021

Mathematical Problems in Engineering

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The conjugate gradient method is a useful method to solve large-scale unconstrained optimisation problems and to be used in some applications in several fields such as engineering, medical science, image restorations, neural network, and many others. The main benefit of the conjugate gradient method is not using the second derivative or its approximation, such as Newton’s method or its approximation. Moreover, the algorithm of the conjugate gradient method is simple and easy to apply. This study proposes a new modified conjugate gradient method that contains four terms depending on popular two- and three-term conjugate gradient methods. The new algorithm satisfies the descent condition. In addition, the new CG algorithm possesses the convergence property. In the numerical results part, we compare the new algorithm with famous methods such as CG-Descent. We conclude from numerical results that the new algorithm is more efficient than other popular CG methods such as CG-Descent 6.8 in terms of number of function evaluations, number of gradient evaluations, number of iterations, and CPU time.

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An improved Dai‐Liao‐style hybrid conjugate gradient‐based method for solving unconstrained nonconvex optimization and extension to constrained nonlinear monotone equations

Yuan,

Shao,

Zeng

et al. 2024

Math Methods in App Sciences

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In this work, for unconstrained optimization, we introduce an improved Dai‐Liao‐style hybrid conjugate gradient method based on the hybridization‐based self‐adaptive technique, and the search direction generated fulfills the sufficient descent and trust region properties regardless of any line search. The global convergence is established under standard Wolfe line search and common assumptions. Then, combining the hyperplane projection technique and a new self‐adaptive line search, we extend the proposed conjugate gradient method and obtain an improved Dai‐Liao‐style hybrid conjugate gradient projection method to solve constrained nonlinear monotone equations. Under mild conditions, we obtain its global convergence without Lipschitz continuity. In addition, the convergence rates for the two proposed methods are analyzed, respectively. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods.

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Some three-term conjugate gradient methods with the new direction structure

Cited by 18 publications

References 30 publications

A three-term conjugate gradient descent method with some applications

A three-term conjugate gradient descent method with some applications

A Descent Four-Term Conjugate Gradient Method with Global Convergence Properties for Large-Scale Unconstrained Optimisation Problems

An improved Dai‐Liao‐style hybrid conjugate gradient‐based method for solving unconstrained nonconvex optimization and extension to constrained nonlinear monotone equations

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