Robust solutions to box-constrained stochastic linear variational inequality problem

Luo, Meiju; Zhang, Yan

doi:10.1186/s13660-017-1529-2

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…In 1966, Hartman and Stampacchia [24] first introduced the variational inequality problem (VIP) for used in the study of partial differential equations with unilateral boundary conditions and free boundary value problems of elliptic type from mechanics. The VIP has been intensively and wildly studied and it has been found that it also can be applied to real world problems such as equilibrium problems, optimal control problems, machine learning, signal processing and linear inverse problems (see, for example, [15,16,29,30,34,37,50]).…”

Section: Introductionmentioning

confidence: 99%

Analysis of two versions of relaxed inertial algorithms with Bregman divergences for solving variational inequalities

et al. 2022

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In this paper, we introduce and analyze two new inertial-like algorithms with the Bregman divergence for solving the pseudomonotone variational inequality problem in a real Hilbert space. The first algorithm is inspired by the Halpern-type iteration and the subgradient extragradient method and the second algorithm is inspired by the Halperntype iteration and Tseng's extragradient method. Under suitable conditions, we prove some strong convergence theorems of the proposed algorithms without assuming the

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Section: Introductionmentioning

confidence: 99%

Analysis of two versions of relaxed inertial algorithms with Bregman divergences for solving variational inequalities

et al. 2022

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“…In 1966, Hartman and Stampacchia [21] first introduced the variational inequality problem (VIP) for used in the study of partial differential equations with unilateral boundary conditions and free boundary value problems of elliptic type from mechanics. The VIP has been intensively and wildly studied and it has been found that it also can be applied to real world problems such as equilibrium problems, optimal control problems, machine learning, signal processing and linear inverse problems (see, for example, [14,15,26,27,31,34,46]).…”

Section: Introductionmentioning

confidence: 99%

Halpern-type relaxed inertial algorithms with Bregman divergence for solving variational inequalities

Jolaoso

Sunthrayuth

Cholamjiak

et al. 2021

Preprint

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It is well-known that the use of Bregman divergence is an elegant and effective technique for solving many problems in applied sciences. In this paper, we introduce and analyze two new inertial-like algorithms with Bregman divergence for solving pseudomonotone variational inequalities in a real Hilbert space. The first algorithm is inspired by Halpern -type iteration and subgradient extragradient method and the second algorithm is inspired by Halpern -type iteration and Tseng's extragradient method. Under suitable conditions, the strong convergence theorems of the algorithms are established without assuming the Lipschitz continuity and the sequential weak continuity of any mapping. Finally, several numerical experiments with various types of Bregman divergence are also performed to illustrate the theoretical analysis. The results presented in this paper improve and generalize the related works in the literature.

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Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications

Chuasuk

Kaewcharoen

2021

Mathematics

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In this article, we discuss the hierarchical fixed point and split monotone variational inclusion problems and propose a new iterative method with the inertial terms involving a step size to avoid the difficulty of calculating the operator norm in real Hilbert spaces. A strong convergence theorem of the proposed method is established under some suitable control conditions. Furthermore, the proposed method is modified and used to derive a scheme for solving the split problems. Finally, we compare and demonstrate the efficiency and applicability of our schemes for numerical experiments as well as an example in the field of image restoration.

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Robust solutions to box-constrained stochastic linear variational inequality problem

Cited by 4 publications

References 19 publications

Analysis of two versions of relaxed inertial algorithms with Bregman divergences for solving variational inequalities

Analysis of two versions of relaxed inertial algorithms with Bregman divergences for solving variational inequalities

Halpern-type relaxed inertial algorithms with Bregman divergence for solving variational inequalities

Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications

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