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New hybrid conjugate gradient projection method for the convex constrained equations

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Abstract

Based on the two famous Hestenes–Stiefel and Dai–Yuan conjugate gradient methods, a new hybrid conjugate gradient projection method is proposed for the convex constrained equations. At each iteration, the new method is fully free from any derivative evaluations. Furthermore, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Under the condition that the underlying mapping is continuous and monotone, we establish the global convergence of the new method. Compared with traditional methods for solving such problem, our new method does not require the Lipschitz continuity of the underlying mapping. Some large-scale numerical tests are performed and reported, which show that the proposed method is efficient and promising.

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Acknowledgments

The authors gratefully acknowledge the helpful comments and suggestions of the anonymous reviewers. This work is supported by the National Natural Science Foundation of China (71371139, 11302188), the Shanghai Shuguang Talent Project (13SG24), the Shanghai Pujiang Talent Project (12PJC069), the foundation of Scientific Research Project of Shandong Universities (J15LI11), and the foundation of Zaozhuang University (2014YB03).

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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, Zhejiang, 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. New hybrid conjugate gradient projection method for the convex constrained equations. Calcolo 53, 399–411 (2016). https://doi.org/10.1007/s10092-015-0154-z

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  • DOI: https://doi.org/10.1007/s10092-015-0154-z

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