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Weak and strong convergence theorems for variational inequality problems

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Abstract

In this paper, we study the weak and strong convergence of two algorithms for solving Lipschitz continuous and monotone variational inequalities. The algorithms are inspired by Tseng’s extragradient method and the viscosity method with Armijo-like step size rule. The main advantages of our algorithms are that the construction of solution approximations and the proof of convergence of the algorithms are performed without the prior knowledge of the Lipschitz constant of cost operators. Finally, we provide numerical experiments to show the efficiency and advantage of the proposed algorithms.

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Acknowledgments

The authors are grateful to the anonymous referees for valuable suggestions which helped to improve the manuscript.

Funding

The first author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.02-2017.15.

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Authors and Affiliations

  1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Duong Viet Thong

  2. Department of Mathematics, College of Air Force, Nha Trang, Vietnam

    Dang Van Hieu

Authors
  1. Duong Viet Thong
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  2. Dang Van Hieu
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Correspondence to Duong Viet Thong.

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Thong, D.V., Hieu, D.V. Weak and strong convergence theorems for variational inequality problems. Numer Algor 78, 1045–1060 (2018). https://doi.org/10.1007/s11075-017-0412-z

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  • DOI: https://doi.org/10.1007/s11075-017-0412-z

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