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A new self-adaptive iterative method for variational inclusion problems on Hadamard manifolds with applications

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Abstract

The objective of this work is to design a new iterative method based on Armijo’s type-modified extragradient method for solving the inclusion problem \(\varvec{(A+B)^{-1}(0)}\), where \(\varvec{A}\) is a maximal monotone vector field and \(\varvec{B}\) is a continuous monotone vector field. The proposed method requires one projection at each iteration, reducing the cost of computational viewpoint and improving the convergence rate. A convergence theorem is established for the proposed extragradient method, significantly improving existing results. We provide concrete examples of Hadamard manifolds and convergency for numerical confirmation. Moreover, we demonstrate convergence results for the variational inequality problems in which the vector field’s monotonicity can be removed.

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Acknowledgements

The authors are thankfully acknowlwdge the suggestions of the anonymous referee.

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Authors and Affiliations

  1. Department of Mathematics, Banaras Hindu University, 221005, Varanasi, India

    Sahu D. R. & Sharma Shikher

  2. Department of Mathematics, University Centre for Research & Development, Chandigarh University, 140413, Mohali, India

    Babu Feeroz

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  1. Sahu D. R.
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  2. Babu Feeroz
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The authors contributed equally and significantly in writing this paper.

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Correspondence to Babu Feeroz.

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D. R., S., Feeroz, B. & Shikher, S. A new self-adaptive iterative method for variational inclusion problems on Hadamard manifolds with applications. Numer Algor 94, 1435–1460 (2023). https://doi.org/10.1007/s11075-023-01542-9

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