A new inexact alternating directions method for monotone variational inequalities

Bingsheng He*, Lizhi LIAO, Deren Han, Hai Yang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

335 Citations (Scopus)


The alternating directions method (ADM) is an effective method for solving a class of variational inequalities (VI) when the proximal and penalty parameters in sub-VI problems are properly selected. In this paper, we propose a new ADM method which needs to solve two strongly monotone sub-VI problems in each iteration approximately and allows the parameters to vary from iteration to iteration. The convergence of the proposed ADM method is proved under quite mild assumptions and flexible parameter conditions.

Original languageEnglish
Pages (from-to)103-118
Number of pages16
JournalMathematical Programming
Issue number1
Publication statusPublished - Mar 2002

Scopus Subject Areas

  • Software
  • Mathematics(all)

User-Defined Keywords

  • Alternating directions method
  • Inexact method
  • Variational inequality


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