A modified extra-gradient method for a family of strongly pseudomonotone equilibrium problems in real Hilbert spaces

Rehman, Habib ur; Pakkaranang, Nuttapol; Hussain, Azhar; Wairojjana, Nopparat

doi:10.22436/jmcs.022.01.04

Cited by 11 publications

(6 citation statements)

References 21 publications

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“…The expression (10) and (11) with Lemma 2.3, provides that limit of x n − p * exists. The sequences {x n }, {w n } and {y n } are bounded.…”

Section: Algorithmmentioning

confidence: 97%

“…One of the most interesting and effective areas of research in equilibrium problem theory is the development of new iterative methods, the improvement of existing methods, and the examination of their convergence analysis. Several methods have already been used in recent years to estimate the solution of the problem of equilibrium in both finite and infinite-dimensional spaces, i.e., the extragradient methods [6,7,8,9,9,10,11,12,13,14,15,16] and others in [17,18,19,20,21,22,23,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modified Popov's Subgradient Extragradient Algorithm With Inertial Technique for Equilibrium Problems and Its Applications

Wairojjana¹,

Rehman²,

Pakkaranang³

et al. 2020

Int. J. of Appl. Math.

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“…The expression (10) and (11) with Lemma 2.3, provides that limit of x n − p * exists. The sequences {x n }, {w n } and {y n } are bounded.…”

Section: Algorithmmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Modified Popov's Subgradient Extragradient Algorithm With Inertial Technique for Equilibrium Problems and Its Applications

Wairojjana¹,

Rehman²,

Pakkaranang³

et al. 2020

Int. J. of Appl. Math.

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“…while Lipschitz constants c 1 = c 2 = 1 2 A − B (see for more details [7,46,47]). The set C ⊂ R 5 is C := {u ∈ R 5 : −5 ≤ u i ≤ 5}.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Convergence Analysis of Self-Adaptive Inertial Extra-Gradient Method for Solving a Family of Pseudomonotone Equilibrium Problems with Application

et al. 2020

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In this article, we propose a new modified extragradient-like method to solve pseudomonotone equilibrium problems in real Hilbert space with a Lipschitz-type condition on a bifunction. This method uses a variable stepsize formula that is updated at each iteration based on the previous iterations. The advantage of the method is that it operates without prior knowledge of Lipschitz-type constants and any line search method. The weak convergence of the method is established by taking mild conditions on a bifunction. In the context of an application, fixed-point theorems involving strict pseudo-contraction and results for pseudomonotone variational inequalities are considered. Many numerical results have been reported to explain the numerical behavior of the proposed method.

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“…and P = Q − S) and vector q entries taken from interval [−n, n] (for more details see [36,47]). The starting points are x −1 = x 0 = (1, 1, • • • , 1) T ∈ R n and µ = 0.22, θ n = 0.20 with β n = 0.85.…”

Section: Numerical Experimentsmentioning

confidence: 99%

A Weak Convergence Self-Adaptive Method for Solving Pseudomonotone Equilibrium Problems in a Real Hilbert Space

2020

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In this paper, we presented a modification of the extragradient method to solve pseudomonotone equilibrium problems involving the Lipschitz-type condition in a real Hilbert space. The method uses an inertial effect and a formula for stepsize evaluation, that is updated for each iteration based on some previous iterations. The key advantage of the algorithm is that it is achieved without previous knowledge of the Lipschitz-type constants and also without any line search procedure. A weak convergence theorem for the proposed method is well established by assuming mild cost bifunction conditions. Many numerical experiments are presented to explain the computational performance of the method and to equate them with others.

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A modified extra-gradient method for a family of strongly pseudomonotone equilibrium problems in real Hilbert spaces

Cited by 11 publications

References 21 publications

Modified Popov's Subgradient Extragradient Algorithm With Inertial Technique for Equilibrium Problems and Its Applications

Modified Popov's Subgradient Extragradient Algorithm With Inertial Technique for Equilibrium Problems and Its Applications

Convergence Analysis of Self-Adaptive Inertial Extra-Gradient Method for Solving a Family of Pseudomonotone Equilibrium Problems with Application

A Weak Convergence Self-Adaptive Method for Solving Pseudomonotone Equilibrium Problems in a Real Hilbert Space

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