A new type of descent conjugate gradient method with exact line search

Hajar, Nurul; Mamat, Mustafa; Rivaie, Mohd; Jusoh, Ibrahim

doi:10.1063/1.4952569

Cited by 11 publications

(8 citation statements)

References 13 publications

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“…An algorithm must satisfy the sufficient descent condition and the global convergence properties. In this case, the global convergence properties are already established in the previous paper [4], so we will just focus on the sufficient descent condition.…”

Section: Convergent Analysismentioning

confidence: 99%

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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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Section: Convergent Analysismentioning

confidence: 99%

“…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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show abstract

“…As a result, most researchers prefer to use inexact line search [11,6,29] which is easier to implement and faster to converge to a solution. In recent years, new computers are equipped with faster processors thus successfully eliminating the speed inefficiency of exact line search as demonstrated by [12,[22][23][24][25]. This encourages more applications of this type of line search in unconstrained optimization [3,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A modified conjugate gradient coefficient under exact line search for unconstrained optimization

Aini¹,

Hajar²,

Rivaie³

et al. 2018

IJET

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The conjugate gradient (CG) method is a well-known solver for large-scale unconstrained optimization problems. In this paper, a modified CG method based on AMR* and CD method is presented. The resulting algorithm for the new CG method is proved to be globally convergent under exact line search both under some mild conditions. Comparisons of numerical performance are made involving the new method and four other CG methods. The results show that the proposed method is more efficient.

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“…In addition, there are many other researchers who conduct studies on CG [8][9][10][11][12] . Regression is used to determine the relationship between two or more variables and use this relationship to make estimation.…”

Section: Introductionmentioning

confidence: 99%

The application of new conjugate gradient methods in estimating data

Shoid¹,

Shapiee²,

Zull³

et al. 2018

IJET

Self Cite

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Many researchers are intended to improve the conjugate gradient (CG) methods as well as their applications in real life. Besides, CG become more interesting and useful in many disciplines and has important role for solving large-scale optimization problems. In this paper, three types of new CG coefficients are presented with application in estimating data. Numerical experiments show that the proposed methods have succeeded in solving problems under strong Wolfe Powell line search conditions.

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A new type of descent conjugate gradient method with exact line search

Cited by 11 publications

References 13 publications

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

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

A modified conjugate gradient coefficient under exact line search for unconstrained optimization

The application of new conjugate gradient methods in estimating data

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