Self-adaptive inertial extragradient algorithms for solving variational inequality problems

Tan, Bing; Fan, Jibin; Li, Songxiao

doi:10.1007/s40314-020-01393-3

Cited by 26 publications

(14 citation statements)

References 20 publications

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“…The following Lemma 5 plays an important role in the convergence analysis of the Algorithm 3.1 and it can be easily obtained by using the same statement as Lemma 3.2 in [28].…”

Section: The Self Adaptive Viscosity-type Inertial Subgradient Extrag...mentioning

confidence: 99%

Self Adaptive Viscosity-Type Inertial Extragradient Algorithms for Solving Variational Inequalities With Applications

Tan

2022

Mathematical Modelling and Analysis

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In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.

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“…The following Lemma 5 plays an important role in the convergence analysis of the Algorithm 3.1 and it can be easily obtained by using the same statement as Lemma 3.2 in [28].…”

Section: The Self Adaptive Viscosity-type Inertial Subgradient Extrag...mentioning

confidence: 99%

Self Adaptive Viscosity-Type Inertial Extragradient Algorithms for Solving Variational Inequalities With Applications

Tan

2022

Mathematical Modelling and Analysis

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“…Note that this small change can greatly accelerate the convergence speed of the iterative algorithm. In recent years, many researchers have studied inertial-type algorithms extensively and have successfully solved many problems, see, e.g., [22,23,24,25,26,27] and the references therein.…”

Section: Figure 1 Comparison Between Iusem-svaiter Methods and Solodov-svaiter Methodsmentioning

confidence: 99%

Inertial extragradient methods for solving pseudomonotone variational inequalities with non-Lipschitz mappings and their optimization applications

2021

Appl. Set-Valued Anal. Optim.

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In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.

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“…In recent years, the development of fast iterative algorithms has aroused great interest from the researchers working in the signal and imaging. They built various fast numerical algorithms by employing the inertial technology, see, for instance, [12,16,29,30,39,40] and the references therein. One of the common features of these algorithms is that the next iteration depends on the combination of the previous two iterations.…”

Section: Introductionmentioning

confidence: 99%

Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

Tan

Yao

2021

J Glob Optim

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This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite-and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.

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Self-adaptive inertial extragradient algorithms for solving variational inequality problems

Cited by 26 publications

References 20 publications

Self Adaptive Viscosity-Type Inertial Extragradient Algorithms for Solving Variational Inequalities With Applications

Self Adaptive Viscosity-Type Inertial Extragradient Algorithms for Solving Variational Inequalities With Applications

Inertial extragradient methods for solving pseudomonotone variational inequalities with non-Lipschitz mappings and their optimization applications

Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

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