New extragradient-like algorithms for strongly pseudomonotone variational inequalities

Hieu, Dang Van; Thong, Duong Viet

doi:10.1007/s10898-017-0564-3

Cited by 52 publications

(9 citation statements)

References 25 publications

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“…(b) Employing analysis which are similar to those for γ after the proof of Theorem 4.1 in [4], we get that the desirable new iterate x k+1 is updated by (21) with γ ∈ [1, 2).…”

Section: Condition 32mentioning

confidence: 99%

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A modified subgradient extragradient method for solving the variational inequality problem

2018

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The subgradient extragradient method for solving the variational inequality (VI) problem, which is introduced by Censor et al. [6], replaces the second projection onto the feasible set of the VI, in the extragradient method, with a subgradient projection onto some constructible half-space. Since the method has been introduced, many authors proposed extensions and modifications with applications to various problems.In this paper, we introduce a modified subgradient extragradient method by improving the stepsize of its second step. Convergence of the proposed method is proved under standard and mild conditions and primary numerical experiments illustrate the performance and advantage of this new subgradient extragradient variant.

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“…(b) Employing analysis which are similar to those for γ after the proof of Theorem 4.1 in [4], we get that the desirable new iterate x k+1 is updated by (21) with γ ∈ [1, 2).…”

Section: Condition 32mentioning

confidence: 99%

“…Since the inception of the subgradient extragradient method, many authors have proposed various modifications, see for example the results [19,8,21]. Kraikaew and Saejung [26] proposed a Halpern-type variant in order to obtain strong convergence, see also [7].…”

Section: Introductionmentioning

confidence: 99%

A modified subgradient extragradient method for solving the variational inequality problem

2018

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“…If the set D is a half-space or a closed ball, effectiveness is completed in the result of the projection onto D. In the recent years, the extragradient method has approved meaningful awareness by numerous authors, who developed it in different ways, see, e.g. [2,3,5] and the several citations therein.…”

Section: Introductionmentioning

confidence: 99%

Approximating $G$-variational inequality problem by $G$-subgradient extragradient method in Hilbert space endowed with graphs

ARAVEEPORN¹,

KHEAWBORISUT²,

Kangtunyakarn³

2022

CJM

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“…Moreover, we introduce a self-adaptive procedure, in the spirit of [47], which generates a sequence of step-sizes converging monotonically to a constant dominating the small step-size in the gradient projection method [17,22]. Comparing with extragradient-type methods [20,40,45], it requires only one projection instead of two. In addition, we further weaken the sequential weak continuity assumption required in recent research [7,38,45,46].…”

Section: Introductionmentioning

confidence: 99%

A New Projection-type Method with Nondecreasing Adaptive Step-sizes for Pseudo-monotone Variational Inequalities

et al. 2022

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We propose a new projection-type method with inertial extrapolation for solving pseudo-monotone and Lipschitz continuous variational inequalities in Hilbert spaces. The proposed method does not require the knowledge of the Lipschitz constant as well as the sequential weak continuity of the corresponding operator. We introduce a self-adaptive procedure, which generates dynamic step-sizes converging to a positive constant. It is proved that the sequence generated by the proposed method converges weakly to a solution of the considered variational inequality with the nonasymptotic O(1/n) convergence rate. Moreover, the linear convergence is established under strong pseudo-monotonicity and Lipschitz continuity assumptions. Numerical examples for solving a class of Nash-Cournot oligopolistic market equilibrium model and a network equilibrium flow problem are given illustrating the efficiency of the proposed method.

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New extragradient-like algorithms for strongly pseudomonotone variational inequalities

Cited by 52 publications

References 25 publications

A modified subgradient extragradient method for solving the variational inequality problem

A modified subgradient extragradient method for solving the variational inequality problem

Approximating $G$-variational inequality problem by $G$-subgradient extragradient method in Hilbert space endowed with graphs

A New Projection-type Method with Nondecreasing Adaptive Step-sizes for Pseudo-monotone Variational Inequalities

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