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A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds

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Abstract

In this paper, we propose an algorithm for finding a zero of a pseudomonotone vector field with a convex constraint on a Hadamard manifold. This new method is the combination of the hyperplane projection method with specially constructed search directions. The global convergence property of this algorithm is established under the assumptions that the constructed halfspace is closed and convex, the tangent vector field is continuous, and the solution set is nonempty. Numerical experiments show the efficiency of this new derivative-free iterative method.

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Acknowledgements

We are very grateful to the two anonymous referees for their valuable comments on the paper, which have considerably improved the paper.

Funding

The research of Zhi Zhao is supported by the Zhejiang Provincial Natural Science Foundation of China (No. LY21A010010) and the National Natural Science Foundation of China (No. 11601112). The research of Ya-Guan Qian is supported by National Key R&D Program of China (No. 2018YFB2100400). The research of Teng-Teng Yao is supported by the Zhejiang Provincial Natural Science Foundation of China (No. LY21A010004) and The National Natural Science Foundation of China (No. 11701514).

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Authors and Affiliations

  1. Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou, 310018, People’s Republic of China

    Zhi Zhao, Qin Zeng & Yu-Nong Xu

  2. Department of Mathematics, School of Sciences, Zhejiang University of Science and Technology, Hangzhou, 310023, People’s Republic of China

    Ya-Guan Qian & Teng-Teng Yao

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  1. Zhi Zhao
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  2. Qin Zeng
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Correspondence to Teng-Teng Yao.

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Zhao, Z., Zeng, Q., Xu, YN. et al. A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds. Numer Algor 93, 1209–1223 (2023). https://doi.org/10.1007/s11075-022-01464-y

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  • DOI: https://doi.org/10.1007/s11075-022-01464-y

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