Abstract
In this paper, we propose a new method, which is set up by incorporating an inertial step with the extragradient method for solving a strongly pseudomonotone equilibrium problems. This method had to comply with a strongly pseudomonotone property and a certain Lipschitz-type condition of a bifunction. A strong convergence result is provided under some mild conditions, and an iterative sequence is accomplished without previous knowledge of the Lipschitz-type constants of a cost bifunction. A sufficient explanation is that the method operates with a slow-moving stepsize sequence that converges to zero and non-summable. For numerical explanations, we analyze a well-known equilibrium model to support our well-established convergence result, and we can see that the proposed method seems to have a significant consistent improvement over the performance of the existing methods.
Highlights
Let C to be a nonempty closed, convex subset of E and f : E × E → R is a bifunction such that f (u, u) = 0 for all u ∈ C
The strategy of the proximal point method was originally developed by Martinet [10] for the problems of a monotone variational inequality, and later Rockafellar [11] developed this idea for monotone operators
By relying on the research work of Hieu et al [30] and Vinh et al [38], we introduce an inertial extragradient method for solving a specific class of equilibrium problems, where f can be a strongly pseudomonotone bifunction
Summary
Iterative methods are basic and powerful tools for studying the numerical solution of an equilibrium problem. In this direction, two well-established approaches are used, i.e., the proximal point method [8] and the auxiliary problem principle [9]. Numerical reviews suggest that inertial effects often improve the performance of the algorithm in terms of the number of iterations and time of execution in this context These two impressive advantages enhance the researcher’s interest in developing new inertial methods. By relying on the research work of Hieu et al [30] and Vinh et al [38], we introduce an inertial extragradient method for solving a specific class of equilibrium problems, where f can be a strongly pseudomonotone bifunction.
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