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The Tikhonov regularization for vector equilibrium problems

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Abstract

We consider vector equilibrium problems in real Banach spaces and study their regularized problems. Based on cone continuity and generalized convexity properties of vector-valued mappings, we propose general conditions that guarantee existence of solutions to such problems in cases of monotonicity and nonmonotonicity. First, our study indicates that every Tikhonov trajectory converges to a solution to the original problem. Then, we establish the equivalence between the problem solvability and the boundedness of any Tikhonov trajectory. Finally, the convergence of the Tikhonov trajectory to the least-norm solution of the original problem is discussed.

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Acknowledgements

The authors are very grateful to the Editors and anonymous Referees for their helpful remarks and suggestions that helped us significantly improve the presentation of the paper. The research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2020.11

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Authors and Affiliations

  1. Department of Mathematics, Teacher College, Cantho University, Can Tho, Vietnam

    Lam Quoc Anh

  2. Department of Mathematics, FPT University, Can Tho, Vietnam

    Tran Quoc Duy

  3. TIMAS, Thang Long University, Hanoi, Vietnam

    Le Dung Muu

  4. Department of Mathematics, Faculty of Science, University of Ostrava, 30 Dubna 22, Ostrava, Czech Republic

    Truong Van Tri

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  1. Lam Quoc Anh
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Correspondence to Tran Quoc Duy.

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Anh, L.Q., Duy, T.Q., Muu, L.D. et al. The Tikhonov regularization for vector equilibrium problems. Comput Optim Appl 78, 769–792 (2021). https://doi.org/10.1007/s10589-020-00258-z

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