A modified conjugate gradient coefficient with inexact line search for unconstrained optimization

Aini, Nurul; Rivaie, Mohd; Mamat, Mustafa

doi:10.1063/1.4968158

Cited by 10 publications

(7 citation statements)

References 11 publications

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“…The CPU processor used was Intel (R) Core TM i3-M350 (2.27GHz) with RAM 4 GB. (5,5), (20,20),(50,50) 8 TRECANNI 2 (5,5), (10,10),(50,50) 9 EXTENDED WOOD 4 (5,..,5), (20,..,20), (30,..,30) 10 CLOVILLE 4 (2,..,2),(4,..,4),(10,..,10) 11 HAGER 2 4 (7,7), (15,15),(22,) (7,..,7), (15,..,15), ( (15,15), (30,30),(150,150) (15,.,15), (30,..,30),(150,..,150) 16 EXTENDED PENALTY (1,1), (5,5),(10,10) (1,..,1),(5,..,5),(10,..,10) 23 EXTENDED TRIDIAGONAL1 2 10,100,1000 (6,6), (12,12),(17,17) (6,..,6), (12,..,12), (17,..,17) 24 DIAGONAL 4 2 10,100,1000…”

Section: Resultsmentioning

confidence: 99%

“…(1,1), (20,20),(40,40) (1,..,1), (20,..,20),(40,..,40) 25 EXTENDED HIMMELBLAU 2 10,100,1000 (10,10),(50,50),(125,125) (10,..,10),(50,..,50),(125,..,125) 26 FLETCHCR 2 10,100,1000 (3,3), (12,12), (15,15) (3,..,3), (12,..,12), (15,..,15) 27 EXTENDED DENSCHNB 2 10,100,1000 (5,5), (30,30),(50,50) (5,..,5), (30,..,30),(50,..,50) 28 EXTENDED BLOCK DIAG-ONAL BD1 2 10,100,1000…”

Section: Resultsmentioning

confidence: 99%

“…Many researchers have studied conjugate gradient method, but the most important properties they well-studied are sufficient condition, global convergence. For example: In [15] proposed her conjugate gradient parameter method which is an extension of LS method and the resulting algorithm was proven to have both the sufficient descent and global convergence properties under inexact line search as follows , where For non-quadratic objective functions, the global convergence property of all methods in Table 2 was proved when an exact line search was used.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solving a large scale nonlinear unconstrained optimization problems by using new coefficient of conjugate gradient method with exact line search direction

Alkouli¹,

Mamat²,

Rivaie³

et al. 2018

IJET

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In this paper, an efficient modification of nonlinear conjugate gradient method and an associated implementation, based on an exact line search, are proposed and analyzed to solve large-scale unconstrained optimization problems. The method satisfies the sufficient descent property. Furthermore, global convergence result is proved. Computational results for a set of unconstrained optimization test problems, some of them from CUTE library, showed that this new conjugate gradient algorithm seems to converge more stable and outperforms the other similar methods in many situations.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solving a large scale nonlinear unconstrained optimization problems by using new coefficient of conjugate gradient method with exact line search direction

Alkouli¹,

Mamat²,

Rivaie³

et al. 2018

IJET

Self Cite

View full text Add to dashboard Cite

show abstract

“…For good comparative studies on newer CG methods, please refer to [15][16][17][18][19]. For newer studies on the optimization method, please refer to [20][21]. Inspired by the spectral method proposed by [22][23] combined the advantages of spectral CG method and FR CG method and presented the modified FR (MFR) method.…”

Section: Introductionmentioning

confidence: 99%

An application of conjugate gradient method under strong Wolfe line search for solving unconstrained optimization

Khadijah¹,

Rivaie²,

Mamat³

et al. 2018

IJET

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The conjugate gradient (CG) method is one of the most prominent methods for solving linear and nonlinear problems in optimization. In this paper, we propose a CG method with sufficient descent property under strong Wolfe line search. The proposed CG method is then applied to solve systems of linear equations. The numerical results obtained from the tests are evaluated based on number iteration and CPU time and then analyzed through performance profile. In order to examine its efficiency, the performance of our CG formula is compared to that of other CG methods. The results show that the proposed CG formula has better performance than the other tested CG methods.

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“…The above methods are known as Fletcher-Reeves (FR) [1], Hestenes-Stiefel (HS) [2] and NPRP [3]. Further reading on new methods can be referred to [4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

A new modified conjugate gradient coefficient for solving system of linear equations

Hajar

Aini

Shapiee

et al. 2017

J. Phys.: Conf. Ser.

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Abstract. Conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. This approach is easy to implement due to its simplicity and has been proven to be effective in solving real-life application. Although this field has received copious amount of attentions in recent years, some of the new approaches of CG algorithm cannot surpass the efficiency of the previous versions. Therefore, in this paper, a new CG coefficient which retains the sufficient descent and global convergence properties of the original CG methods is proposed. This new CG is tested on a set of test functions under exact line search. Its performance is then compared to that of some of the well-known previous CG methods based on number of iterations and CPU time. The results show that the new CG algorithm has the best efficiency amongst all the methods tested. This paper also includes an application of the new CG algorithm for solving large system of linear equations

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A modified conjugate gradient coefficient with inexact line search for unconstrained optimization

Cited by 10 publications

References 11 publications

Solving a large scale nonlinear unconstrained optimization problems by using new coefficient of conjugate gradient method with exact line search direction

Solving a large scale nonlinear unconstrained optimization problems by using new coefficient of conjugate gradient method with exact line search direction

An application of conjugate gradient method under strong Wolfe line search for solving unconstrained optimization

A new modified conjugate gradient coefficient for solving system of linear equations

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