Forward-backward-based descent methods for composite variational inequalities

Bingsheng He, Xiaoming YUAN*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


We consider the monotone composite variational inequality (CVI) where the underlying mapping is formed as the sum of two monotone mappings. We combine the forward-backward and descent direction ideas together, and thus present the unified algorithmic framework of forward-backward-based descent methods for solving the CVI. A new iterate of such a method is generated by a prediction-correction fashion, where the predictor is yielded by the forward-backward method and then the predictor is corrected by a descent step. We derive some implementable forward-backward-based descent algorithms for some concrete cases of the CVI, and verify their numerical efficiency via preliminary numerical experiments.

Original languageEnglish
Pages (from-to)706-724
Number of pages19
JournalOptimization Methods and Software
Issue number4
Publication statusPublished - 1 Aug 2013

Scopus Subject Areas

  • Software
  • Control and Optimization
  • Applied Mathematics

User-Defined Keywords

  • composite mapping
  • contraction
  • descent direction
  • forward-backward method
  • variational inequality


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