An inexact proximal decomposition method for variational inequalities with separable structure

Erik A. Papa Quiroz, Orlando Sarmiento, Paulo Roberto Oliveira

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1 Scopus citations


This paper presents an inexact proximal method for solving monotone variational inequality problems with a given separable structure. The proposed algorithm is a natural extension of the Proximal Multiplier Algorithm with Proximal Distances (PMAPD) proposed by Sarmiento et al. [Optimization 65 (2016) 501-537], which unified the works of Chen and Teboulle (PCPM method), and Kyono and Fukushima (NPCPMM) developed for solving convex programs with a particular separable structure. The resulting method combines the recent proximal distances theory introduced by Auslender and Teboulle [SIAM J. Optim. 16 (2006) 697-725] with a decomposition method given by Chen and Teboulle for convex problems and extends the results of the Entropic Proximal Decomposition Method proposed by Auslender and Teboulle, which used to Logarithmic Quadratic proximal distances. Under some mild assumptions on the problem we prove a global convergence of the primal-dual sequences produced by the algorithm.

Original languageEnglish
Pages (from-to)S873-S884
JournalRAIRO - Operations Research
StatePublished - 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© EDP Sciences, ROADEF, SMAI 2021.


  • Maximal monotone operators
  • Proximal distances
  • Separable structure
  • Variational inequalities


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