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A modified Hestenes–Stiefel projection method for constrained nonlinear equations and its linear convergence rate

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Abstract

The Hestenes–Stiefel (HS) method is an efficient method for solving large-scale unconstrained optimization problems. In this paper, we extend the HS method to solve constrained nonlinear equations, and propose a modified HS projection method, which combines the modified HS method proposed by Zhang et al. with the projection method developed by Solodov and Svaiter. Under some mild assumptions, we show that the new method is globally convergent with an Armijo line search. Moreover, the R-linear convergence rate of the new method is established. Some preliminary numerical results show that the new method is efficient even for large-scale constrained nonlinear equations.

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Acknowledgments

The authors would like to thank the referees for giving us many valuable suggestions and comments, which improve this paper greatly. This work was partially supported by the domestic visiting scholar project funding of Shandong Province outstanding young teachers in higher schools, the foundation of Scientific Research Project of Shandong Universities (No. J13LI03), the NSF of Shandong Province, China and the Shandong Province Statistical Research Project (No. 20143038).

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  1. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, Shandong, China

    Min Sun

  2. School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, 310018, China

    Jing Liu

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  1. Min Sun
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  2. Jing Liu
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Correspondence to Min Sun.

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Sun, M., Liu, J. A modified Hestenes–Stiefel projection method for constrained nonlinear equations and its linear convergence rate. J. Appl. Math. Comput. 49, 145–156 (2015). https://doi.org/10.1007/s12190-014-0829-7

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  • DOI: https://doi.org/10.1007/s12190-014-0829-7

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