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Proximal point algorithm for inclusion problems in Hadamard manifolds with applications

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Abstract

This paper deals with the proximal point algorithm for finding a singularity of sum of a single-valued vector field and a set-valued vector field in the setting of Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed. Applications to composite minimization problems and variational inequality problems are also presented.

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Acknowledgements

Authors are grateful to the references for their valuable suggestions and corrections. In this research, first author was supported by a research grant of DST-SERB No. EMR/2016/005124.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Qamrul Hasan Ansari & Feeroz Babu

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Qamrul Hasan Ansari

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  1. Qamrul Hasan Ansari
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  2. Feeroz Babu
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Correspondence to Qamrul Hasan Ansari.

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Ansari, Q.H., Babu, F. Proximal point algorithm for inclusion problems in Hadamard manifolds with applications. Optim Lett 15, 901–921 (2021). https://doi.org/10.1007/s11590-019-01483-0

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