A Novel Value for the Parameter in the Dai-Liao-Type Conjugate Gradient Method

Ivanov, Branislav; Stanimirović, Predrag S.; Shaini, Bilall I.; Ahmad, Harith; Wang, Miao-Kun

doi:10.1155/2021/6693401

Cited by 7 publications

(18 citation statements)

References 23 publications

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“…was introduced in [1] by Dai and Liao. Te condition (18) has been an inspiration for many researchers, of which the most important are Hager and Zhang [24,25], Dai and Kou [26], Babaie-Kafaki and Ghanbari [27], Ivanov et al [28], Lotf and Hosseini [15], and Zheng and Zheng [33] to create new DL-type CG methods. Some of the most signifcant rules to determine t are collected in Table 1.…”

Section: Introduction and Overview Of Related Resultsmentioning

confidence: 99%

“…Te MSMDL method is based on ( 2), ( 6), (28), and (29). Te algorithmic procedure of the MSMDL method is established in Algorithm 2.…”

Section: Parameters T Kmentioning

confidence: 99%

“…To this aim, we perform two competitions on standard test functions with given initial points from [41,42]. Te frst competition is between CG-DESCENT [24], M1 [27], DK [26], and MSMDL methods, and the second one is between BB1DL, MSMDL, and two recently developed DL CG methods with global convergence property (EDL [28] and MDL [15]). We compare all of these methods into three criteria:…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…To complete the theorem, it is necessary to prove that t MSMDL k is bounded. Two cases should be distinguished based on the defnition of t MSMDL k in (28).…”

mentioning

confidence: 99%

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A Modified Dai–Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and Its Application

Ivanov

Milovanović

Stanimirović

et al. 2023

Journal of Mathematics

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We introduce and investigate proper accelerations of the Dai–Liao (DL) conjugate gradient (CG) family of iterations for solving large-scale unconstrained optimization problems. The improvements are based on appropriate modifications of the CG update parameter in DL conjugate gradient methods. The leading idea is to combine search directions in accelerated gradient descent methods, defined based on the Hessian approximation by an appropriate diagonal matrix in quasi-Newton methods, with search directions in DL-type CG methods. The global convergence of the modified Dai–Liao conjugate gradient method has been proved on the set of uniformly convex functions. The efficiency and robustness of the newly presented methods are confirmed in comparison with similar methods, analyzing numerical results concerning the CPU time, a number of function evaluations, and the number of iterative steps. The proposed method is successfully applied to deal with an optimization problem arising in 2D robotic motion control.

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Section: Introduction and Overview Of Related Resultsmentioning

confidence: 99%

“…Te MSMDL method is based on ( 2), ( 6), (28), and (29). Te algorithmic procedure of the MSMDL method is established in Algorithm 2.…”

Section: Parameters T Kmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

“…To complete the theorem, it is necessary to prove that t MSMDL k is bounded. Two cases should be distinguished based on the defnition of t MSMDL k in (28).…”

mentioning

confidence: 99%

See 2 more Smart Citations

A Modified Dai–Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and Its Application

Ivanov

Milovanović

Stanimirović

et al. 2023

Journal of Mathematics

Self Cite

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“…Fletcher and Reeves discussed the non-linear conjugate gradient method in 1964. [18], Several modifications have been introduced by researchers to the CG method, such as (, [19])…”

Section: Introductionmentioning

confidence: 99%

Optimized Trigonometric Spline Function with Conjugate GradientMethod for Solving FDEs

Hamasalh¹,

Sadiq²,

Salam³

2022

JUAPS

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We investigate the non-polynomial spline function to solve the fractional differential equations with the conformable conjugate gradient method. The fractional derivative was described using the Caputo fractional derivative to construct the spline scheme with polynomial fractional order. Therefore, transform the problem to an equivalent iterative linear system that can be solved by Gauss-Seidel and conjugate gradient methods. For the given spline function, error bounds were studied and a stability analysis was completed, the error estimation is also calculated as different values of (n) depend on the step size oh (h). Numerical examples with known analytical solutions are shown to verify the method's accuracy. The outcomes are in satisfactory correlation with the exact answers according to the numerical experiments. Moreover, the convergence analysis was investigated with the drive some theorems. Also, the procedure is explained in depth and supported by computational examples and the results show that the fractional spline function which interpolates data is productive and profitable in solving unique problems and compare with the exact solutions.

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Accelerated Dai-Liao projection method for solving systems of monotone nonlinear equations with application to image deblurring

2022

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A Novel Value for the Parameter in the Dai-Liao-Type Conjugate Gradient Method

Cited by 7 publications

References 23 publications

A Modified Dai–Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and Its Application

A Modified Dai–Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and Its Application

Optimized Trigonometric Spline Function with Conjugate GradientMethod for Solving FDEs

Accelerated Dai-Liao projection method for solving systems of monotone nonlinear equations with application to image deblurring

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