An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems

Tan, Bing; Li, Songxiao

doi:10.1007/s13398-021-01116-1

Cited by 5 publications

(2 citation statements)

References 38 publications

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“…Te authors established that under some appropriate assumptions, the sequence u n 􏼈 􏼉 generated by ( 16) converged strongly to unique solution of BVIP (1). Also, Tan et al [22] introduced and analyzed an accelerated projection and contraction extragradient algorithm for solving bilevel variational inequality problem (1). Tey proposed the iterative method:…”

Section: Introductionmentioning

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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Section: Introductionmentioning

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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“…where θ n ∈ [0, 1) is an extrapolation factor and λ n is a step-size parameter (sufficiently small) and ∇ F is the gradient of a smooth convex function F. The algorithm is more effective and converges faster is because of the term θ n (x n − x n−1 ) in (3) as the inertial step (see Alakoya et al [1], Ceng et al [5], Cholamjiak et al [12], Dong et al [13], Lorenz and Pock [30], Tan et al [44] and Thong et al [46]).…”

Section: Introductionmentioning

confidence: 99%

Variational inequality over the set of common solutions of a system of bilevel variational inequality problem with applications

Eslamian

2021

RACSAM

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In this paper, we study variational inequality problem over the set of common solutions of a system of bilevel variational inequality problem. We present a new and efficient iterative method for solving this problem and establish its strong convergence. As applications, we use our algorithm for solving the multiple set split variational inequality problem, the hierarchical variational inequality problem, the bilevel variational inequality problem and hierarchical minimization problem.

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A strongly convergent algorithm for solving split equality problems beyond monotonicity

Mewomo,

Uzor,

Gibali

2024

Comp. Appl. Math.

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In this paper, we focus on some split inverse problems, namely the split equality variational inequalities and common fixed point problems, and combine various operator theory techniques to establish minimum-norm strong convergence for our proposed method. We present two strong convergent results with (and without) reference to the monotonicity property of the cost operators. Our convergence analyses assume very mild conditions and thus generalize and extend recent related results in the literature. Furthermore, several numerical examples illustrate the practical potentials and advantages of our proposed algorithm.

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An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems

Cited by 5 publications

References 38 publications

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

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

Variational inequality over the set of common solutions of a system of bilevel variational inequality problem with applications

A strongly convergent algorithm for solving split equality problems beyond monotonicity

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