Decomposition method for a class of monotone variational inequality problems

B. S. He*, Lizhi LIAO, H. Yang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


In the solution of the monotone variational inequality problem VI (Ω, F), with (Formula Presented) uJ*l F(u) = \f(x)-ATy\ V = VXV, Iy J IAx-b J the augmented Lagrangian method (a decomposition method) is advantageous and effective when script Y sign = ℛm. For some problems of interest, where both the constraint sets script X sign and script Y sign are proper subsets in ℛn and ℛm, the original augmented Lagrangian method is no longer applicable. For this class of variational inequality problems, we introduce a decomposition method and prove its convergence. Promising numerical results are presented, indicating the effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)603-622
Number of pages20
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - Dec 1999

Scopus Subject Areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

User-Defined Keywords

  • Convergence
  • Decomposition methods
  • Monotone variational inequalities


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