An Algorithm for a Class of Bilevel Variational Inequalities with Split Variational Inequality and Fixed Point Problem Constraints

Hải, Nguyễn Minh; Vân, Lê Huỳnh Mỹ; Anh, Tran Viet

doi:10.1007/s40306-020-00389-9

Cited by 8 publications

(6 citation statements)

References 12 publications

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“…4. Our computational experiments show that our proposed method is efficient and better than the iterative scheme in [20]. 5.…”

mentioning

confidence: 91%

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A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces

Akutsah¹,

Mebawondu²,

Abass³

et al. 2023

NACO

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<p style='text-indent:20px;'>In this work, we propose a new inertial method for solving strongly monotone variational inequality problems over the solution set of a split variational inequality and composed fixed point problem in real Hilbert spaces. Our method uses stepsizes that are generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the operator norm as well as the Lipschitz constant of the operator. In addition, we prove that the proposed method converges strongly to a minimum-norm solution of the problem without using the conventional two cases approach. Furthermore, we present some numerical experiments to show the efficiency and applicability of our method in comparison with other methods in the literature. The results obtained in this paper extend, generalize and improve results in this direction.</p>

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“…4. Our computational experiments show that our proposed method is efficient and better than the iterative scheme in [20]. 5.…”

mentioning

confidence: 91%

“…In 2020, the authors in [20], considered the problem (9), proposed the following iterative algorithm and established a strong convergence theorem.…”

mentioning

confidence: 99%

A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces

Akutsah¹,

Mebawondu²,

Abass³

et al. 2023

NACO

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“…From the knowledge of (3) emerged another interesting extension and generalization of VIP (2) known as split variational inequality and fxed-point problem (SVIFPP) introduced by Hai et al in [9]. Tis notion involves Find u * ∈ D which solves 〈G u * 􏼁, u − u * 〉 ≥ 0, ∀u ∈ D, (6)…”

Section: Introductionmentioning

confidence: 99%

“…Inspired by the work of Mainge, the authors in [9] introduced and analyzed iterative algorithm for solving another special form of (1) as given in the following: Find u * ∈ Ω such that 〈F u * 􏼁, u − u * 〉 ≥ 0, ∀u ∈ Ω, (13) where Ω:…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems

Abuchu

Ofem

Ugwunnadi

et al. 2023

Journal of Mathematics

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This paper considers an alternated inertial-type extrapolation algorithm for solving bilevel pseudomonotone variational inequality problem in the framework of real Hilbert spaces with split variational inequality and fixed-point constraints of demimetric mapping. The algorithm which involves alternated inertial uses self-adjustment stepsize condition that depends solely on the information from previous iterative step. The bilevel problem considered in the work consists of upper-level problem with an underlying operator which is pseudomonotone, while the lower problem is associated with strongly monotone mapping and the fixed-point constraint of demimetric mapping. Our algorithm is anchored on modified projection and contraction techniques, fused with alternated inertial and relaxation. Under some suitable conditions on the algorithm control parameters, we obtain a strong convergence result of the proposed method without the prior knowledge of the operator norm or the coefficients of the underlying operators within the scope of real Hilbert spaces. Finally, some numerical examples are presented to illustrate the gain of our method in comparison to some related algorithms in the literature.

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Inertial extrapolation method with regularization for solving a new class of bilevel problem in real Hilbert spaces

Akutsah

Mebawondu

Ugwunnadi

et al. 2022

SeMA

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An Algorithm for a Class of Bilevel Variational Inequalities with Split Variational Inequality and Fixed Point Problem Constraints

Cited by 8 publications

References 12 publications

A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces

A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces

Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems

Inertial extrapolation method with regularization for solving a new class of bilevel problem in real Hilbert spaces

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