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The Tikhonov regularization for vector equilibrium problems

Author

Listed:
  • Lam Quoc Anh

    (Cantho University)

  • Tran Quoc Duy

    (FPT University)

  • Le Dung Muu

    (Thang Long University)

  • Truong Van Tri

    (University of Ostrava)

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.

Suggested Citation

  • Lam Quoc Anh & Tran Quoc Duy & Le Dung Muu & Truong Van Tri, 2021. "The Tikhonov regularization for vector equilibrium problems," Computational Optimization and Applications, Springer, vol. 78(3), pages 769-792, April.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:3:d:10.1007_s10589-020-00258-z
    DOI: 10.1007/s10589-020-00258-z
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    References listed on IDEAS

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