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New Bregman projection methods for solving pseudo-monotone variational inequality problem

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Abstract

In this work, we introduce two Bregman projection algorithms with self-adaptive stepsize for solving pseudo-monotone variational inequality problem in a Hilbert space. The weak and strong convergence theorems are established without the prior knowledge of Lipschitz constant of the cost operator. The convergence behavior of the proposed algorithms with various functions of the Bregman distance are presented. More so, the performance and efficiency of our methods are compared to other related methods in the literature.

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Funding

P. Cholamjiak thanks School of Science, University of Phayao and Thailand Science Research and Innovation (IRN62W0007).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani, 12110, Thailand

    Pongsakorn Sunthrayuth

  2. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria, South Africa

    Lateef Olakunle Jolaoso

  3. School of Science, University of Phayao, Mae Ka, Phayao, 56000, Thailand

    Prasit Cholamjiak

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  1. Pongsakorn Sunthrayuth
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  2. Lateef Olakunle Jolaoso
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  3. Prasit Cholamjiak
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Correspondence to Prasit Cholamjiak.

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Sunthrayuth, P., Jolaoso, L.O. & Cholamjiak, P. New Bregman projection methods for solving pseudo-monotone variational inequality problem. J. Appl. Math. Comput. 68, 1565–1589 (2022). https://doi.org/10.1007/s12190-021-01581-2

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