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2017•Journal of Inequalities and ApplicationsOpen access

Dai-Kou type conjugate gradient methods with a line search only using gradient

Yuanyuan Huang, Changhe Liu

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Abstract

In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope. Under suitable conditions, the developed methods are globally convergent. Numerical tests and comparisons with the PRP+ conjugate gradient method only using gradient show that the methods are efficient.

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What this paper is about

In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope. Under suitable conditions, the developed methods are globally convergent. Numerical tests and comparisons with the PRP+ conjugate gradient method only using gradient show that the methods are efficient.

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Available abstract

In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope. Under suitable conditions, the developed methods are globally convergent. Numerical tests and comparisons with the PRP+ conjugate gradient method only using gradient show that the methods are efficient.

Key concepts: Conjugate gradient method, Nonlinear conjugate gradient method, Derivation of the conjugate gradient method, Conjugate residual method, Mathematics, Gradient method, Biconjugate gradient method, Proximal Gradient Methods

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