An improved BFGS search direction using exact line search for solving unconstrained optimization problems

Sofi, Azfi Zaidi Mohammad; Mamat, Mustafa; Mohd, İsmail

doi:10.12988/ams.2013.13007

Cited by 7 publications

(6 citation statements)

References 21 publications

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“…Table 1 below is the unconstrained optimization tested problems and most of them can be seen in [17]. Two points were selected for each of the problem as can be seen in Table 1 Table 2 show the numerical result for quasi-Newton method using 8 10 as stopping criteria value except for Maratos function which we use 6 10 . In this paper, both QN and CGSD-QN use the DFP update formula.…”

Section: Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Conjugate gradient and steepest descent approach on quasi-Newton search direction

Sofi¹,

Mamat²,

Mohd³

et al. 2014

AIP Conference Proceedings

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Abstract. An approach of using conjugate gradient and classic steepest descent search direction onto quasi-Newton search direction had been proposed in this paper and we called it as 'scaled CGSD-QN' search direction. A new coefficient formula had been successfully constructed for being used in the 'scaled CGSD-QN' search direction and proven here that the coefficient formula is globally converge to the minimizer. The Hessian update formula that has been used in the quasi-Newton algorithm is DFP update formula. This new search direction approach was testes with some some standard unconstrained optimization test problems and proven that this new search direction approach had positively affect quasi-Newton method by using DFP update formula.

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Section: Numerical Resultsmentioning

confidence: 99%

“…We can used either one of the inexact line search as suggested by [7] or using the exact line search as suggested by [8] and [9] that is…”

Section: Introductionmentioning

confidence: 99%

Conjugate gradient and steepest descent approach on quasi-Newton search direction

Sofi¹,

Mamat²,

Mohd³

et al. 2014

AIP Conference Proceedings

Self Cite

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show abstract

“…For recent findings and further references of studies on CG method, refer to Andrei [15], Hager and Zang [19], Wei et al [22], Rivaie et al [12,13], Abashar et al [1], Jusoh et al [7], and Sofi et al [18].…”

Section: Introductionmentioning

confidence: 99%

A modified nonlinear conjugate gradient method for unconstrained optimization

Sulaiman¹,

Mamat²,

Abashar³

et al. 2015

ams

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Nonlinear conjugate gradient method holds an important role in solving large scale unconstrained optimization problems. Their simplicity, low memory requirement, and global convergence stimulated a massive study on the method. Numerous modifications have been done recently to improve its performance. In this paper, we proposed a new formula for the conjugate gradient coefficient k  that generates the descent search direction. In addition, we establish the global convergence result under exact line search. The outcome of our numerical experiment show that the proposed formula is very efficient and more reliable when compare to other conjugate gradient methods.

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“…Then the step size, i in (2) was obtained using the exact line search such as proposed by [11] and [12] where >0 arg min ( )…”

Section: Introductionmentioning

confidence: 99%

Fletcher Reeves like CG formula approach on Broyden family update

Sofi¹,

Mamat²,

Mohd³

et al. 2014

AIP Conference Proceedings

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The Broyden family update in quasi-Newton method is known as one of the most efficient update method in solving unconstrained optimization. However, by using the standard search direction, sometimes the algorithm may lead to the failure for some complicated problems and this scenario worsen when the cases of the initial points selected are far away from the minimizer. To overcome this scenario, we proposed a new search direction by using the Fletcher Reeves formula in the conjugate gradient method to be fit with the new search direction. We proved that this new search direction globally converge and positively affect the Broyden family update in quasi-Newton method.

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An improved BFGS search direction using exact line search for solving unconstrained optimization problems

Cited by 7 publications

References 21 publications

Conjugate gradient and steepest descent approach on quasi-Newton search direction

Conjugate gradient and steepest descent approach on quasi-Newton search direction

A modified nonlinear conjugate gradient method for unconstrained optimization

Fletcher Reeves like CG formula approach on Broyden family update

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