The extragradient algorithm with inertial effects extended to equilibrium problems

Rehman, Habib ur; Kumam, Poom; Abubakar, Auwal Bala; Cho, Yeol Je

doi:10.1007/s40314-020-1093-0

Cited by 49 publications

(23 citation statements)

References 27 publications

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“…The development of new iterative methods and the examination of their converging analysis are among the most effective and valuable research directions in equilibrium theory. Several numerical results for solving the problem of equilibrium in different abstract spaces have been established (for instance, see [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]).…”

Section: Introductionmentioning

confidence: 99%

The Inertial Sub-Gradient Extra-Gradient Method for a Class of Pseudo-Monotone Equilibrium Problems

et al. 2020

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In this article, we focus on improving the sub-gradient extra-gradient method to find a solution to the problems of pseudo-monotone equilibrium in a real Hilbert space. The weak convergence of our method is well-established based on the standard assumptions on a bifunction. We also present the application of our results that enable to solve numerically the pseudo-monotone and monotone variational inequality problems, in addition to the particular presumptions required by the operator. We have used various numerical examples to support our well-proved convergence results, and we can show that the proposed method involves a considerable influence over-running time and the total number of iterations.

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Section: Introductionmentioning

confidence: 99%

The Inertial Sub-Gradient Extra-Gradient Method for a Class of Pseudo-Monotone Equilibrium Problems

et al. 2020

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“…Furthermore, Konnov [12] also provides a different variant of the proximal point method with weaker assumptions in the case of equilibrium problems. Several numerical methods based on these techniques have been developed to solve different classes of equilibrium problems in finite and infinite-dimensional abstract spaces (for more details see, [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]). More specifically, Hieu et al in [30] developed an iterative sequence sequence {u n } recursively as…”

Section: Introductionmentioning

confidence: 99%

Inertial Extra-Gradient Method for Solving a Family of Strongly Pseudomonotone Equilibrium Problems in Real Hilbert Spaces with Application in Variational Inequality Problem

et al. 2020

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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.

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“…Many researchers have provided and generalized many results corresponding to the existence of a solution for the equilibrium problem (see [7][8][9][10]). A considerable number of methods are the earliest set up over the last few years concentrating on the different equilibrium problem classes and other particular forms of an equilibrium problem in abstract spaces (see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]).…”

Section: Introductionmentioning

confidence: 99%

A Self-Adaptive Extra-Gradient Methods for a Family of Pseudomonotone Equilibrium Programming with Application in Different Classes of Variational Inequality Problems

et al. 2020

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The main objective of this article is to propose a new method that would extend Popov’s extragradient method by changing two natural projections with two convex optimization problems. We also show the weak convergence of our designed method by taking mild assumptions on a cost bifunction. The method is evaluating only one value of the bifunction per iteration and it is uses an explicit formula for identifying the appropriate stepsize parameter for each iteration. The variable stepsize is going to be effective for enhancing iterative algorithm performance. The variable stepsize is updating for each iteration based on the previous iterations. After numerical examples, we conclude that the effect of the inertial term and variable stepsize has a significant improvement over the processing time and number of iterations.

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The extragradient algorithm with inertial effects extended to equilibrium problems

Cited by 49 publications

References 27 publications

The Inertial Sub-Gradient Extra-Gradient Method for a Class of Pseudo-Monotone Equilibrium Problems

The Inertial Sub-Gradient Extra-Gradient Method for a Class of Pseudo-Monotone Equilibrium Problems

Inertial Extra-Gradient Method for Solving a Family of Strongly Pseudomonotone Equilibrium Problems in Real Hilbert Spaces with Application in Variational Inequality Problem

A Self-Adaptive Extra-Gradient Methods for a Family of Pseudomonotone Equilibrium Programming with Application in Different Classes of Variational Inequality Problems

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