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An improved Perry conjugate gradient method with adaptive parameter choice

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Abstract

In this paper, we present a conjugate gradient method for solving unconstrained optimization problems. Motivated by Perry conjugate gradient method and Dai-Liao method, an improved Perry update matrix is proposed to overcome the non-symmetric positive definite property of the Perry matrix. The parameter in the update matrix is determined by minimizing the condition number of the iterative matrix which can ensure the positive definite property. The obtained method can also be considered as a modified form of CG-DESCENT method with an adjusted term. Under some mild conditions, the presented method is global convergent. Numerical experiments under CUTEst environment show that the proposed algorithm is promising.

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Acknowledgments

Guangxi Universities Foundation Grant no: KY2015YB268.

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Authors and Affiliations

  1. Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, 530003, China

    Shengwei Yao, Donglei He & Lihua Shi

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  1. Shengwei Yao
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  2. Donglei He
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  3. Lihua Shi
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Correspondence to Shengwei Yao.

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Yao, S., He, D. & Shi, L. An improved Perry conjugate gradient method with adaptive parameter choice. Numer Algor 78, 1255–1269 (2018). https://doi.org/10.1007/s11075-017-0422-x

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