Abstract
In this paper, we introduce a new step size strategy for projection-type algorithms for solving strongly pseudomonotone equilibrium problems in a Hilbert space. In contrast to the work by Anh et al. (Numer Algorithms. https://doi.org/10.1007/s11075-018-0578-z, 2017) and by Santos et al. (Comput Appl Math 30:91–107, 2011), our methods do not require the step sizes being square summable. Moreover, at each step of the proposed algorithms, instead of solving a constrained problem, we only have to solve an unconstrained problem and compute a projection onto the feasible set or its intersection with a closed sphere. The strong convergence of the proposed algorithms is proven without any Lipschitz-type condition. Also, we evaluate the convergence rate of these algorithms. Using cutting hyperplanes, we refine the feasible set at the beginning of our algorithms. Thanks to this, we can apply the new algorithms to the equilibrium problems with non-closed and non-convex feasible set. Some numerical experiments and comparisons confirm efficiency of the proposed modification.
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The authors would like to thanks the editor and the referee for valuable remarks and helpful suggestions which improved the quality of the paper.
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Communicated by Orizon Pereira Ferreira.
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Hai, T.N. Convergence rate of a new projected-type algorithm solving non-Lipschitz equilibrium problems. Comp. Appl. Math. 39, 52 (2020). https://doi.org/10.1007/s40314-020-1062-7
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DOI: https://doi.org/10.1007/s40314-020-1062-7