# Weak convergence for variational inequalities with inertial-type method

@article{Shehu2020WeakCF, title={Weak convergence for variational inequalities with inertial-type method}, author={Yekini Shehu and Olaniyi Samuel Iyiola}, journal={Applicable Analysis}, year={2020}, volume={101}, pages={192 - 216} }

Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods.

## 2 Citations

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In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our…

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## References

SHOWING 1-10 OF 78 REFERENCES

Iterative method with inertial for variational inequalities in Hilbert spaces

- MathematicsCalcolo
- 2018

Strong convergence property for Halpern-type iterative method with inertial terms for solving variational inequalities in real Hilbert spaces is investigated under mild assumptions in this paper. Our…

Convergence analysis of projection method for variational inequalities

- MathematicsComput. Appl. Math.
- 2019

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert…

Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators

- Mathematics
- 2015

We propose a modified extragradient method with dynamic step size adjustment to solve variational inequalities with monotone operators acting in a Hilbert space. In addition, we consider a version of…

An extragradient-like approximation method for variational inequality problems and fixed point problems

- MathematicsAppl. Math. Comput.
- 2007

Inertial projection and contraction algorithms for variational inequalities

- MathematicsJ. Glob. Optim.
- 2018

A modified version of the algorithm to find a common element of the set of solutions of a variational inequality and theset of fixed points of a nonexpansive mapping in H.

Strong convergence of a double projection-type method for monotone variational inequalities in Hilbert spaces

- Mathematics
- 2018

We introduce a projection-type algorithm for solving monotone variational inequality problems in real Hilbert spaces without assuming Lipschitz continuity of the corresponding operator. We prove that…

A hybrid method without extrapolation step for solving variational inequality problems

- MathematicsJ. Glob. Optim.
- 2015

A new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space based on well-known projection method and the hybrid (or outer approximation) method is introduced.

Modified hybrid projection methods for finding common solutions to variational inequality problems

- MathematicsComput. Optim. Appl.
- 2017

Several modified hybrid projection methods for solving common solutions to variational inequality problems involving monotone and Lipschitz continuous operators using differently constructed half-spaces are proposed.

An Inertial Forward-Backward Algorithm for Monotone Inclusions

- Mathematics, Computer ScienceJournal of Mathematical Imaging and Vision
- 2014

An inertial forward-backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive, inspired by the accelerated gradient method of Nesterov.

Convergence of One-Step Projected Gradient Methods for Variational Inequalities

- MathematicsJ. Optim. Theory Appl.
- 2016

This paper revisits the numerical approach to some classical variational inequalities, with monotone and Lipschitz continuous mapping A, by means of a projected reflected gradient-type method and establishes the convergence of the method in a more general setting that allows to use varying step-sizes without any requirement of additional projections.