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Enhanced Dai–Liao conjugate gradient methods for systems of monotone nonlinear equations

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Abstract

In this paper, we propose two conjugate gradient methods for solving large-scale monotone nonlinear equations. The methods are developed by combining the hyperplane projection method by Solodov and Svaiter (Reformulation: nonsmooth, piecewise smooth, semismooth and smoothing methods. Springer, pp 355–369, 1998) and two modified search directions of the famous Dai and Liao (Appl Math Optim 43(1): 87–101, 2001) method. It is shown that the proposed schemes satisfy the sufficient descent condition. The global convergence of the methods are established under mild conditions, and computational experiments on some benchmark test problems show that the methods are promising.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Science, Bayero University, Kano, Kano, Nigeria

    M. Y. Waziri & K. Ahmed

  2. Department of Mathematics, Faculty of Sciences, Yusuf Maitama Sule University, Kano, Kano, Nigeria

    J. Sabi’u

  3. Department of Mathematics and Computer Science, Sule Lamido University, Kafin Hausa, Nigeria

    A. S. Halilu

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  1. M. Y. Waziri
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  2. K. Ahmed
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  3. J. Sabi’u
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  4. A. S. Halilu
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Waziri, M.Y., Ahmed, K., Sabi’u, J. et al. Enhanced Dai–Liao conjugate gradient methods for systems of monotone nonlinear equations. SeMA 78, 15–51 (2021). https://doi.org/10.1007/s40324-020-00228-9

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