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A spectral three-term Hestenes–Stiefel conjugate gradient method

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Abstract

In this paper, according to some suitable features of three-term conjugate gradient methods and excellent theoretical properties of the quasi-Newton methods, a new spectral three-term conjugate gradient is proposed. A modified secant condition is used to compute a suitable spectral parameter. The new search direction ensures the sufficient descent condition without any line search. It is established that the new scheme possesses the global convergence, under the strong Wolfe conditions. Preliminary numerical experiments show the efficiency of the new method, dealing with unconstrained optimization problems.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran

    Parvaneh Faramarzi & Keyvan Amini

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  1. Parvaneh Faramarzi
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  2. Keyvan Amini
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Correspondence to Keyvan Amini.

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Faramarzi, P., Amini, K. A spectral three-term Hestenes–Stiefel conjugate gradient method. 4OR-Q J Oper Res 19, 71–92 (2021). https://doi.org/10.1007/s10288-020-00432-3

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  • DOI: https://doi.org/10.1007/s10288-020-00432-3

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