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Analysis and Mathematical Physics

, Volume 9, Issue 4, pp 2203–2225 | Cite as

Two simple projection-type methods for solving variational inequalities

  • Aviv Gibali
  • Duong Viet ThongEmail author
  • Pham Anh Tuan
Article
Part of the following topical collections:
  1. Perspectives in Modern Analysis

Abstract

In this paper we study a classical monotone and Lipschitz continuous variational inequality in real Hilbert spaces. Two projection type methods, Mann and its viscosity generalization are introduced with their strong convergence theorems. Our methods generalize and extend some related results in the literature and their main advantages are: the strong convergence and the adaptive step-size usage which avoids the need to know apriori the Lipschitz constant of variational inequality associated operator. Primary numerical experiments in finite and infinite dimensional spaces compare and illustrate the behaviors of the proposed schemes.

Keywords

Projection-type method Variational inequality Mann-type method Viscosity method Projection and contraction method 

Mathematics Subject Classification

47H09 47J20 65K15 90C25 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Aviv Gibali
    • 1
    • 2
  • Duong Viet Thong
    • 3
    Email author
  • Pham Anh Tuan
    • 4
  1. 1.Department of MathematicsORT Braude CollegeKarmielIsrael
  2. 2.The Center for Mathematics and Scientific ComputationUniversity of HaifaMt. Carmel, HaifaIsrael
  3. 3.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  4. 4.Faculty of Economics MathematicsNational Economics UniversityHanoi CityVietnam

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