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An efficient three-term conjugate gradient method for nonlinear monotone equations with convex constraints

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Abstract

In this paper, based on the hyperplane projection technique, we propose a three-term conjugate gradient method for solving nonlinear monotone equations with convex constraints. Due to the derivative-free feature and lower storage requirement, the proposed method can be applied to the solution of large-scale non-smooth nonlinear monotone equations. Under some mild assumptions, the global convergence is proved when the line search fulfils the backtracking line search condition. Moreover, we prove that the proposed method is R-linearly convergent. Numerical results show that our method is competitive and efficient for solving large-scale nonlinear monotone equations with convex constraints.

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Acknowledgements

The authors gratefully acknowledge the helpful comments and suggestions of the anonymous reviewers.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Peiting Gao & Chuanjiang He

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  1. Peiting Gao
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  2. Chuanjiang He
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Correspondence to Chuanjiang He.

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This research was partially supported by the Chinese National Science Foundation (NSFC61561019 and NSFC11371384) and Chongqing Graduate Student Research Innovation Project (CYS14020).

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Gao, P., He, C. An efficient three-term conjugate gradient method for nonlinear monotone equations with convex constraints. Calcolo 55, 53 (2018). https://doi.org/10.1007/s10092-018-0291-2

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