Conjugate Gradient ‎Method: A Developed Version to Resolve Unconstrained Optimization Problems

Alhawarat, Ahmad; Nguyen-Thoi, Trung; Salleh, Zabidin

doi:10.3844/jcssp.2020.1220.1228

Cited by 3 publications

(5 citation statements)

References 18 publications

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“…where 3) with the CG method in equation (28), where the step size satisfies (4) and (5). en, we obtain the results by using Lemmas 2 and 3, as well as Lemmas 4.1 and 4.2 in [10], where liminf k⟶∞ ‖g k ‖ � 0.…”

Section: Global Convergence Of Figure 1 With General Nonlinearmentioning

confidence: 66%

“…Meanwhile, for (y k− 1 + s k− 1 ), the direction y k− 1 is an essential term in obtaining the descent condition when multiplied by negative gradient. It is also useful in terms of efficiency, i.e., if this term goes to zero, the search direction will restart using the steepest descent method, avoiding equation (28) to cycle without reaching the solution.…”

Section: The New Search Directionmentioning

confidence: 99%

“…e Descent Property of the New Search Direction. e following theorem shows that the search direction in equation (28) ensures that the sufficient descent condition ( 35) is satisfied with the SWP line search. Theorem 1.…”

Section: 1mentioning

confidence: 99%

“…Moreover, the CG method can be applied in several fields: neural network, image restoration, medical science, machine learning, finance and economics, and many other fields. e reader can refer to [26][27][28][29][30][31][32][33][34][35][36] for more about the CG method and its applications.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Global Convergence Of Figure 1 With General Nonlinearmentioning

confidence: 66%

Section: The New Search Directionmentioning

confidence: 99%

Section: 1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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

Self Cite

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“…Yousif et al [27] introduced a criterion that ensures the establishment of the descent search direction property and the global convergence of CG techniques under SW line search. Many researchers (see e.g., Refs [28][29][30][31][32]) have demonstrated that several numerical techniques for unconstrained optimization converge under the SW condition.…”

Section: Introductionmentioning

confidence: 99%

Global convergence properties of a Dai-Liao-type CGM for unconstrained optimization

Onuoha

2024

Recent Adv. Nat. Sci

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A popular optimization technique called the conjugate gradient method (CGM) is renowned for its effectiveness in addressing problems involving unconstrained optimization. Several conjugate gradient (CG) techniques have been proven to possess global convergence properties both theoretically and numerically. The Dai-Liao-type CGM is a variant that incorporates certain modifications to enhance its convergence properties. This paper examines the global convergence properties of a Dai-Liao-type CGM for unconstrained optimization problems. Theoretically, this study investigates the conditions under which the method ensures convergence to the global minimum of the objective function, focusing on the algorithm’s descent directions, the necessary reduction in objective function values, and termination criteria. A numerical experiment is conducted on a set of unconstrained optimization problems to validate the theoretical results obtained in this work. The numerical findings of this study demonstrate the robustness and reliability of the Dai-Liao-type CGM, showing its ability to find the global optimal solution in a wide range of unconstrained optimization problems.

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A decent three term conjugate gradient method with global convergence properties for large scale unconstrained optimization problems

Masmali¹,

Salleh

Alhawarat

2021

MATH

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<abstract> <p>The conjugate gradient (CG) method is a method to solve unconstrained optimization problems. Moreover CG method can be applied in medical science, industry, neural network, and many others. In this paper a new three term CG method is proposed. The new CG formula is constructed based on DL and WYL CG formulas to be non-negative and inherits the properties of HS formula. The new modification satisfies the convergence properties and the sufficient descent property. The numerical results show that the new modification is more efficient than DL, WYL, and CG-Descent formulas. We use more than 200 functions from CUTEst library to compare the results between these methods in term of number of iterations, function evaluations, gradient evaluations, and CPU time.</p> </abstract>

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Conjugate Gradient ‎Method: A Developed Version to Resolve Unconstrained Optimization Problems

Cited by 3 publications

References 18 publications

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

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

Global convergence properties of a Dai-Liao-type CGM for unconstrained optimization

A decent three term conjugate gradient method with global convergence properties for large scale unconstrained optimization problems

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