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2018•International Journal of Engineering & TechnologyOpen access

A New Conjugate Gradient Method with Exact Line Search

Mouiyad Bani Yousef, Mustafa Mamat, Mohd Rivaie

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Abstract

The nonlinear conjugate gradient (CG) method is a widely used approach for solving large-scale optimization problems in many fields, such as physics, engineering, economics, and design. The efficiency of this method is mainly attributable to its global convergence properties and low memory requirement. In this paper, a new conjugate gradient coefficient is proposed based on the Aini-Rivaie-Mustafa (ARM) method. Furthermore, the proposed method is proved globally convergent under exact line search. This is supported by the results of the numerical tests. The numerical performance of the new CG method better than other related and more efficient compared with previous CG methods.

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What this paper is about

The nonlinear conjugate gradient (CG) method is a widely used approach for solving large-scale optimization problems in many fields, such as physics, engineering, economics, and design. The efficiency of this method is mainly attributable to its global convergence properties and low memory requirement. In this paper, a new conjugate gradient coefficient is proposed based on the Aini-Rivaie-Mustafa (ARM) method. Furthermore, the proposed method is proved globally convergent under exact line search. This is supported by the results of the numerical tests. The numerical performance of the new CG method better than other related and more efficient compared with previous CG methods.

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Available abstract

The nonlinear conjugate gradient (CG) method is a widely used approach for solving large-scale optimization problems in many fields, such as physics, engineering, economics, and design. The efficiency of this method is mainly attributable to its global convergence properties and low memory requirement. In this paper, a new conjugate gradient coefficient is proposed based on the Aini-Rivaie-Mustafa (ARM) method. Furthermore, the proposed method is proved globally convergent under exact line search. This is supported by the results of the numerical tests. The numerical performance of the new CG method better than other related and more efficient compared with previous CG methods.

Key concepts: Conjugate gradient method, Nonlinear conjugate gradient method, Line search, Conjugate residual method, Derivation of the conjugate gradient method, Convergence (economics), Gradient method, Conjugate

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