Convergence analysis of projection method for variational inequalities

  • Yekini ShehuEmail author
  • Olaniyi S. Iyiola
  • Xiao-Huan Li
  • Qiao-Li Dong


The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is monotone and uniformly continuous. We carry out a unified analysis of the proposed method under very mild assumptions. In particular, weak convergence of the generated sequence is established and nonasymptotic O(1 / n) rate of convergence is established, where n denotes the iteration counter. We also present some experimental results to illustrate the profits gained by introducing the inertial extrapolation steps.


Variational inequalities Inertial extrapolation step Monotone operator Hilbert spaces 

Mathematics Subject Classification

47H05 47J20 47J25 65K15 90C25 



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© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China
  2. 2.Institute of Science and Technology (IST)KlosterneuburgAustria
  3. 3.Department of MathematicsComputer Science and Information Systems, California University of PennsylvaniaPAUSA
  4. 4.College of ScienceCivil Aviation University of ChinaTianjinChina

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