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A New Hybrid HS-DY Conjugate Gradient Method

Junli Dong, Baocong Jiao, Lanping Chen

Open publisher page 9 citations

Abstract

Conjugate gradient method is one of the most useful methods for solving unconstrained optimization problem. In this paper, we propose a hybrid conjugate gradient method for unconstrained optimization based on the Hestenes-Stiefel and Dai-Yuan conjugate gradient Algorithms. By searching a particular direction, the new algorithm satisfies the descent condition. Furthermore under the Wolfe line search conditions, we prove that the new method can support the global convergence. The initial numerical experiments show that the new algorithm is efficient.

About this research paper

What this paper is about

Conjugate gradient method is one of the most useful methods for solving unconstrained optimization problem. In this paper, we propose a hybrid conjugate gradient method for unconstrained optimization based on the Hestenes-Stiefel and Dai-Yuan conjugate gradient Algorithms. By searching a particular direction, the new algorithm satisfies the descent condition. Furthermore under the Wolfe line search conditions, we prove that the new method can support the global convergence. The initial numerical experiments show that the new algorithm is efficient.

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OpenAlex reports 9 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Conjugate gradient method is one of the most useful methods for solving unconstrained optimization problem. In this paper, we propose a hybrid conjugate gradient method for unconstrained optimization based on the Hestenes-Stiefel and Dai-Yuan conjugate gradient Algorithms. By searching a particular direction, the new algorithm satisfies the descent condition. Furthermore under the Wolfe line search conditions, we prove that the new method can support the global convergence. The initial numerical experiments show that the new algorithm is efficient.

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

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