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[<jats:italic>Optimization<\/jats:italic> <jats:bold>65<\/jats:bold> (2016) 501\u2013537], 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 [<jats:italic>SIAM J. Optim<\/jats:italic>. <jats:bold>16<\/jats:bold> (2006) 697\u2013725] 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\u2013dual sequences produced by the algorithm.<\/jats:p>","DOI":"10.1051\/ro\/2020018","type":"journal-article","created":{"date-parts":[[2020,2,20]],"date-time":"2020-02-20T04:40:08Z","timestamp":1582173608000},"page":"S873-S884","source":"Crossref","is-referenced-by-count":1,"special_numbering":"Supplement","title":["An inexact proximal decomposition method for variational inequalities with separable structure"],"prefix":"10.1051","volume":"55","author":[{"given":"Erik A.","family":"Papa Quiroz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Orlando","family":"Sarmiento","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paulo Roberto","family":"Oliveira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2021,3,2]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s101070100241","volume":"91","author":"Auslender","year":"2001","journal-title":"Math. 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