Improved inertial projection and contraction method for solving pseudomonotone variational inequality problems

The objective of this article is to solve pseudomonotone variational inequality problems in a real Hilbert space. We introduce an inertial algorithm with a new self-adaptive step size rule, which is based on the projection and contraction method. Only one step projection is used to design the propos...

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Bibliographic Details
Published in:Journal of inequalities and applications 2021-06, Vol.2021 (1), p.1-20, Article 107
Main Authors: Tian, Ming, Xu, Gang
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
Convergence
Cost analysis
Hilbert space
Inertial method
Iterative methods
Mathematical analysis
Mathematics
Mathematics and Statistics
Projection
Projection and contraction method
Pseudomonotone mapping
Self-adaptive technique
Variational inequality problem
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Summary:The objective of this article is to solve pseudomonotone variational inequality problems in a real Hilbert space. We introduce an inertial algorithm with a new self-adaptive step size rule, which is based on the projection and contraction method. Only one step projection is used to design the proposed algorithm, and the strong convergence of the iterative sequence is obtained under some appropriate conditions. The main advantage of the algorithm is that the proof of convergence of the algorithm is implemented without the prior knowledge of the Lipschitz constant of cost operator. Numerical experiments are also put forward to support the analysis of the theorem and provide comparisons with related algorithms.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02643-6