Journal of Global Optimization

, Volume 70, Issue 2, pp 385–399 | Cite as

New extragradient-like algorithms for strongly pseudomonotone variational inequalities

  • Dang Van HieuEmail author
  • Duong Viet Thong


The paper considers two extragradient-like algorithms for solving variational inequality problems involving strongly pseudomonotone and Lipschitz continuous operators in Hilbert spaces. The projection method is used to design the algorithms which can be computed more easily than the regularized method. The construction of solution approximations and the proof of convergence of the algorithms are performed without the prior knowledge of the modulus of strong pseudomonotonicity and the Lipschitz constant of the cost operator. Instead of that, the algorithms use variable stepsize sequences which are diminishing and non-summable. The numerical behaviors of the proposed algorithms on a test problem are illustrated and compared with those of several previously known algorithms.


Variational inequality problem Monotone operator Pseudomonotone operator Strongly monotone operator Strongly pseudomonotone operator Extragradient method Subgradient extragradient method Projection method 

Mathematics Subject Classification

65Y05 65K15 68W10 47H05 47H10 



The authors would like to thank the Associate Editor and two anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. The first author was partially supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.315. The second author was partially funded by NAFOSTED under Grant No. 101.02-2017.15 and by Vietnam Institute for Advanced Study in Mathematics (VIASM).


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsCollege of Air ForceNha Trang CityVietnam
  2. 2.Faculty of Economics MathematicsNational Economics UniversityHanoi CityVietnam

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