The convergence properties of some descent conjugate gradient algorithms for optimization models

Sulaiman, Ibrahim Mohammed; Mamat, Mustafa; Owoyemi, Abiodun Ezekiel; Ghazali, Puspa Liza; Rivaie, Mohd; Malik, Maulana

doi:10.22436/jmcs.022.03.02

Cited by 8 publications

(9 citation statements)

References 11 publications

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“…Using Lemma 1 and estimate (27), we can obtain the first inequality of expression (18). Nevertheless, ρ(y t ) and ρ(x t ) are monotonically decreasing.…”

Section: Ball Convergencementioning

confidence: 98%

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Convergence Criteria of a Three-Step Scheme under the Generalized Lipschitz Condition in Banach Spaces

et al. 2022

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In the given study, we investigate the three-step NTS’s ball convergence for solving nonlinear operator equations with a convergence order of five in a Banach setting. A nonlinear operator’s first-order derivative is assumed to meet the generalized Lipschitz condition, also known as the κ-average condition. Furthermore, several theorems on the convergence of the same method in Banach spaces are developed with the conditions that the derivative of the operators must satisfy the radius or center-Lipschitz condition with a weak κ-average and that κ is a positive integrable but not necessarily non-decreasing function. This novel approach allows for a more precise convergence analysis even without the requirement for new circumstances. As a result, we broaden the applicability of iterative approaches. The theoretical results are supported further by illuminating examples. The convergence theorem investigates the location of the solution ϵ* and the existence of it. In the end, we achieve weaker sufficient convergence criteria and more specific knowledge on the position of the ϵ* than previous efforts requiring the same computational effort. We obtain the convergence theorems as well as some novel results by applying the results to some specific functions for κ(u). Numerical tests are carried out to corroborate the hypotheses established in this work.

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“…Using Lemma 1 and estimate (27), we can obtain the first inequality of expression (18). Nevertheless, ρ(y t ) and ρ(x t ) are monotonically decreasing.…”

Section: Ball Convergencementioning

confidence: 98%

“…All z t belong to ( * , δ) by mathematical induction, and ρ(z t ) = z t − * decreases monotonically. Lastly, simplifying the first result in the inequality of expression (18), we obtain…”

Section: Ball Convergencementioning

confidence: 99%

Convergence Criteria of a Three-Step Scheme under the Generalized Lipschitz Condition in Banach Spaces

et al. 2022

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“…12 Ex -Rosenbrock 100,1000 (11,11), (13,13) 14 Ex Tridiagonal 1 100, 1000,10000 (12,12), (17,17),(20,2 0),(30,30) 5…”

Section: Applicationmentioning

confidence: 99%

“…In fact, Powell [11], [12] gave some counter examples to show that even with the exact minimization condition, there exist some functions, for which PRP method fails to converge. For more reference on convergence properties of recent CG algorithms, please refer to [13], [14]. Recently, Rivaie et al [15] proposed a new variant of the PRP method known as RMIL which represent the researcher's name: Rivaie-Mustafa-Ismail-Leong.…”

Section: Introductionmentioning

confidence: 99%

A new hybrid conjugate gradient algorithm for optimization models and its application to regression analysis

Sulaiman

Bakar²,

Mamat³

et al. 2021

IJEECS

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The hybrid conjugate gradient (CG) method is among the efficient variants of CG method for solving optimization problems. This is due to their low memory requirements and nice convergence properties. In this paper, we present an efficient hybrid CG method for solving unconstrained optimization models and show that the method satisfies the sufficient descent condition. The global convergence prove of the proposed method would be established under inexact line search. Application of the proposed method to the famous statistical regression model describing the global outbreak of the novel COVID-19 is presented. The study parameterized the model using the weekly increase/decrease of recorded cases from December 30, 2019 to March 30, 2020. Preliminary numerical results on some unconstrained optimization problems show that the proposed method is efficient and promising. Furthermore, the proposed method produced a good regression equation for COVID-19 confirmed cases globally.

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“…The beneficial effects of three-term CG have encouraged more investigations of its application to the RMIL method. The following are some of the three-term versions of RMIL methods termed as ttRMIL+, ttRMIL and ttRMIL* proposed in [28]- [30], respectively.…”

Section: Introductionmentioning

confidence: 99%

A new three-term conjugate gradient method with application to regression analysis

Idalisa

Rivaie²,

Noh³

et al. 2022

IJECE

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Conjugate gradient (CG) method is well-known for its ability to solve unconstrained optimization (UO.) problems. This article presenting a new CG method with sufficient descent conditions which improves the former method developed by Rvaie, Mustafa, Ismail and Leong (RMIL). The efficacy of the proposed method has been demonstrated through simulations on the Kijang Emas pricing regression problem. The daily data between January 2021 to May 2021 were obtained from Malaysian Ministry of Health and Bank Negara Malaysia. The dependent variable for this study was the Kijang Emas price, and the independent variables were the coronavirus disease (COVID-19) measures (i.e., new cases, R-naught, death cases, new recovered). Data collected were analyzed on its correlation and coefficient determinant, and the influences of COVID-19 on Kijang Emas price was examined through multiple linear regression model. Findings revealed that the suggested technique outperformed the existing CG algorithms in terms of computing efficiency.

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The convergence properties of some descent conjugate gradient algorithms for optimization models

Cited by 8 publications

References 11 publications

Convergence Criteria of a Three-Step Scheme under the Generalized Lipschitz Condition in Banach Spaces

Convergence Criteria of a Three-Step Scheme under the Generalized Lipschitz Condition in Banach Spaces

A new hybrid conjugate gradient algorithm for optimization models and its application to regression analysis

A new three-term conjugate gradient method with application to regression analysis

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