Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space

Yair Censor, Aviv Gibali, Simeon Reich

Research output: Contribution to journalArticlepeer-review

Abstract

We study two projection algorithms for solving the variational inequality problem in Hilbert space. One algorithm is a modified subgradient extragradient method in which an additional projection onto the intersection of two half-spaces is employed. Another algorithm is based on the shrinking projection method. We establish strong convergence theorems for both algorithms.

Original languageEnglish
Pages (from-to)827-845
Number of pages19
JournalOptimization Methods and Software
Volume26
Issue number4-5
DOIs
StatePublished - Aug 2011

Bibliographical note

Funding Information:
We are very grateful to two anonymous referees whose insightful comments helped us to considerably improve an earlier version of this paper. This work was partially supported by Award Number R01HL070472 from the National Heart, Lung and Blood Institute, by the United States–Israel Binational Science Foundation (BSF), Grant number 200912, by the Israel Science Foundation (ISF), Grant number 647/07 and by the Fund for the Promotion of Research at the Technion and the Technion President’s Research Fund.

Keywords

  • extragradient method
  • Hilbert space
  • projection algorithm
  • subgradient
  • variational inequality

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics

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