A Dai–Liao conjugate gradient method via modified secant equation for system of nonlinear equations

Waziri, Mohammed Yusuf; Ahmed, Kabiru; Sabi’u, Jamilu

doi:10.1007/s40065-019-0264-6

Cited by 36 publications

(25 citation statements)

References 60 publications

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“…One of todays' best performing CG method is Dai & Liao (DL) method which depends on non-negative parameter t for its computation. Although numerous optimal selections for the parameter were suggested as in (Babaie-Kafaki, & Ghanbari 2014b;Babaie-Kafaki,2015;Babaie-Kafaki & Ghanbari, 2017;Waziri, et al, 2019;Salihu, et al, 2021), the best choice of t still remains subject of consideration (Babaie-Kafaki, & Ghanbari, 2015). Motivated by the above, in this section, using similar approach in (Andrei, 2008b;Andrei, 2009;Babaie-Kafaki, et al, 2010;Djordjevic, 2017), this research will combine the attractive features of CG update parameters proposed by Liu and Storey (1991) with CG parameter proposed by Fletcher (1987) conjugate descent using Extended Conjugacy Condition of Dai and Liao (2001) CG method called (ECCDL) as follows:…”

Section: Extended Conjugacy Condition Of Dai and Liao Cg Methods (Eccdl)mentioning

confidence: 99%

A dai-liao hybrid conjugate gradient method for unconstrained optimization

Salihu

Odekunle

Waziri

et al. 2021

Int. J. Ind. Optim.

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One of todays’ best-performing CG methods is Dai-Liao (DL) method which depends on non-negative parameter and conjugacy conditions for its computation. Although numerous optimal selections for the parameter were suggested, the best choice of remains a subject of consideration. The pure conjugacy condition adopts an exact line search for numerical experiments and convergence analysis. Though, a practical mathematical experiment implies using an inexact line search to find the step size. To avoid such drawbacks, Dai and Liao substituted the earlier conjugacy condition with an extended conjugacy condition. Therefore, this paper suggests a new hybrid CG that combines the strength of Liu and Storey and Conjugate Descent CG methods by retaining a choice of Dai-Liao parameterthat is optimal. The theoretical analysis indicated that the search direction of the new CG scheme is descent and satisfies sufficient descent condition when the iterates jam under strong Wolfe line search. The algorithm is shown to converge globally using standard assumptions. The numerical experimentation of the scheme demonstrated that the proposed method is robust and promising than some known methods applying the performance profile Dolan and Mor´e on 250 unrestricted problems. Numerical assessment of the tested CG algorithms with sparse signal reconstruction and image restoration in compressive sensing problems, file restoration, image video coding and other applications. The result shows that these CG schemes are comparable and can be applied in different fields such as temperature, fire, seismic sensors, and humidity detectors in forests, using wireless sensor network techniques.

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Section: Extended Conjugacy Condition Of Dai and Liao Cg Methods (Eccdl)mentioning

confidence: 99%

A dai-liao hybrid conjugate gradient method for unconstrained optimization

Salihu

Odekunle

Waziri

et al. 2021

Int. J. Ind. Optim.

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“…e researchers continued various updates of the DL-parameter in order to obtain some suitable formulas. See for example [10][11][12]. Moreover, the researcher's Zhang et al [13] prompt a threeterm CG-technique based mostly of the DL-technique as follows:…”

Section: A Modified Dai-liao Three-term Cg Techniquementioning

confidence: 99%

Spectral Three-Term Constrained Conjugate Gradient Algorithm for Function Minimizations

Ahmed

Al-Kawaz²,

Al-Bayati

2019

Journal of Applied Mathematics

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In this work, we tend to deal within the field of the constrained optimization methods of three-term Conjugate Gradient (CG) technique which is primarily based on Dai–Liao (DL) formula. The new proposed technique satisfies the conjugacy property and the descent conditions of Karush–Kuhn–Tucker (K.K.T.). Our planned constrained technique uses the robust Wolfe line search condition with some assumptions. We tend to prove the global convergence property of the new planned technique. Numeral comparisons for (30-thirty) constrained optimization issues make sure the effectiveness of the new planned formula.

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“…, a number of modified forms of the Perry and Dai-Liao methods for nonlinear systems of equations have been proposed [1,4,7,27,28]. These Perry and Dai-Liao methods are based on a quasi-Newton aspect and have been considered to be among the most effective in the context of unconstrained optimization.…”

Section: Introductionmentioning

confidence: 99%

A modified Perry-type derivative-free projection method for solving large-scale nonlinear monotone equations

Koorapetse

Kaelo

Kooepile-Reikeletseng

2021

RAIRO-Oper. Res.

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In this paper, a new modified Perry-type derivative-free projection method for solving large-scale nonlinear monotone equations is presented. The method is developed by combining a modified Perry's conjugate gradient method with the hyperplane projection technique. Global convergence and numerical results of the proposed method are established. Preliminary numerical results show that the proposed method is promising and efficient compared to some existing methods in the literature.

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A Dai–Liao conjugate gradient method via modified secant equation for system of nonlinear equations

Abstract: In this paper, we propose a Dai-Liao (DL) conjugate gradient method for solving large-scale system of nonlinear equations. The method incorporates an extended secant equation developed from modified secant equations proposed by Zhang et al.

Cited by 36 publications

References 60 publications

A dai-liao hybrid conjugate gradient method for unconstrained optimization

A dai-liao hybrid conjugate gradient method for unconstrained optimization

Spectral Three-Term Constrained Conjugate Gradient Algorithm for Function Minimizations

A modified Perry-type derivative-free projection method for solving large-scale nonlinear monotone equations

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