Abstract
We study the extragradient method for solving vector quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for vector equilibrium problems and scalar quasi-equilibrium problems. We propose a regularization procedure which ensures the strong convergence of the generated sequence to a solution of the vector quasi-equilibrium problem under standard assumptions on the problem without assuming neither any monotonicity assumption on the vector valued bifunction nor any weak continuity assumption of f in its arguments that in the many well-known methods have been used. Also, we show that the boundedness of the generated sequences implies that the solution set of the vector quasi-equilibrium problem is nonempty, and prove the strong convergence of the generated sequences to a solution of the problem. Finally, we give some examples of vector quasi-equilibrium problems to which our main theorem can be applied. We also present some numerical experiments.
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Communicated by Orizon Pereira Ferreira.
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Mohebbi, V. Extragradient method with Bregman distances for solving vector quasi-equilibrium problems. Comp. Appl. Math. 41, 376 (2022). https://doi.org/10.1007/s40314-022-02086-9
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DOI: https://doi.org/10.1007/s40314-022-02086-9
Keywords
- Bregman distance
- Extragradient method
- Linesearch
- Quasi \(D_g\)-nonexpansive mapping
- Vector quasi-equilibrium problem
- Vector valued bifunction