On Bilevel Split Pseudomonotone Variational Inequality Problems with Applications

Anh, Pham Ky; Anh, Tran Viet; Mưu, Lê Dũng

doi:10.1007/s40306-016-0178-8

Cited by 23 publications

(11 citation statements)

References 12 publications

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“…(ii) If F and G satisfy properties (A1), (A2) and (A3), (A4) respectively, then the solution sets Sol(C, F) and Sol(Q, G) of the VIP(C, F) and VIP(Q, G) are closed and convex (see e.g., [1,Lemma 6]). Therefore, the solution set Ω = {x * ∈ Sol(C, F) : Ax * ∈ Sol(Q, G)} of the SVIP is also closed and convex.…”

Section: Resultsmentioning

confidence: 99%

Two inertial linesearch extragradient algorithms for the bilevel split pseudomonotone variational inequality with constraints

2020

J. Appl. Numer. Optim.

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Section: Resultsmentioning

confidence: 99%

Two inertial linesearch extragradient algorithms for the bilevel split pseudomonotone variational inequality with constraints

2020

J. Appl. Numer. Optim.

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“…Lemma 2 (see [33,35]). Let H be a real Hilbert space with μ, ] ∈ H and α ∈ R, then the following holds…”

Section: Preliminariesmentioning

confidence: 99%

“…Defnition 1 (see [33,34]). Let H be real Hilbert space and D a nonempty, closed and convex subset of H. Let M: H ⟶ H be a real single-valued mapping and…”

Section: Preliminariesmentioning

confidence: 99%

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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“…Lemma 2.2. [35] Let H be a real Hilbert space, and let F : H → H be a β -strongly monotone and L−Lipschitz continuous mapping on…”

Section: Preliminariesmentioning

confidence: 99%

A modified inertial projection and contraction method for solving bilevel split variational inequality problems

2022

Appl. Set-Valued Anal. Optim.

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The main purpose of this paper is to study a bilevel split variational inequality problem in two real Hilbert spaces. We propose a new modified inertial projection and contraction method for solving this problem when one of the cost operators is pseudomonotone and Lipschitz continuous, but not sequentially weakly continuous. Strong convergence of the proposed method is established and numerical examples are given to support our theoretical findings.

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On Bilevel Split Pseudomonotone Variational Inequality Problems with Applications

Cited by 23 publications

References 12 publications

Two inertial linesearch extragradient algorithms for the bilevel split pseudomonotone variational inequality with constraints

Two inertial linesearch extragradient algorithms for the bilevel split pseudomonotone variational inequality with constraints

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

A modified inertial projection and contraction method for solving bilevel split variational inequality problems

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