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Hybrid Inertial Contraction Algorithms for Solving Variational Inequalities with Fixed Point Constraints in Hilbert Spaces

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Abstract

In this paper, basing on the forward-backward method and inertial techniques, we introduce a new algorithm for solving a variational inequality problem over the fixed point set of a nonexpansive mapping. The strong convergence of the algorithm is established under strongly monotone and Lipschitz continuous assumptions imposed on the cost mapping. As an application, we also apply and analyze our algorithm to solve a convex minimization problem of the sum of two convex functions.

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Acknowledgements

We are very grateful to anonymous referees for their really helpful and constructive comments that helped us very much in improving the paper.

Funding

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2019.303.

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Authors and Affiliations

  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam

    Pham Ngoc Anh

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  1. Pham Ngoc Anh
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Correspondence to Pham Ngoc Anh.

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Anh, P.N. Hybrid Inertial Contraction Algorithms for Solving Variational Inequalities with Fixed Point Constraints in Hilbert Spaces. Acta Math Vietnam 47, 743–753 (2022). https://doi.org/10.1007/s40306-021-00467-6

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