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Convergence theorems for solving a system of pseudomonotone variational inequalities using Bregman distance in Banach spaces

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Abstract

In this paper, we present two new parallel Bregman projection algorithms for finding a common solution of a system of pseudomonotone variational inequality problems in a real reflexive Banach space. The first algorithm combines a parallel Bregman subgradient extragradient method with the Halpern iterative method for approximating a common solution of variational inequalities in reflexive Banach spaces. The second algorithm involves a parallel Bregman subgradient extragradient method, Halpern iterative method and a line search procedure which aims to avoid the condition of finding prior estimate of the Lipschitz constant of each cost operator. Two strong convergence results were proved under standard assumptions imposed on the cost operators and control sequences. Finally, we provide some numerical experiments to illustrate the behaviour of the sequences generated by the proposed algorithms.

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Acknowledgements

This research was completed when LO was visiting the Federal University of Agriculture Abeokuta as a research visitor. The author thanks the institution for providing their resources will aid the research.

Funding

This first author is supported by the Postdoctoral research grant from the Sefako Makgatho Health Sciences University, South Africa.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa, Pretoria, 0204, South Africa

    Lateef Olakunle Jolaoso & Maggie Aphane

  2. Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun, Nigeria

    Lateef Olakunle Jolaoso, Musiliu Tayo Raji, Idowu Ademola Osinuga & Bakai Ishola Olajuwon

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  1. Lateef Olakunle Jolaoso
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  2. Maggie Aphane
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  3. Musiliu Tayo Raji
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  4. Idowu Ademola Osinuga
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  5. Bakai Ishola Olajuwon
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All authors worked equally on the results and approved the final manuscript.

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Correspondence to Lateef Olakunle Jolaoso.

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Jolaoso, L.O., Aphane, M., Raji, M.T. et al. Convergence theorems for solving a system of pseudomonotone variational inequalities using Bregman distance in Banach spaces. Boll Unione Mat Ital 15, 561–588 (2022). https://doi.org/10.1007/s40574-022-00322-y

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