An inexact proximal decomposition method for variational inequalities with separable structure
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2020-02-12Author(s)
Papa Quiroz, Erik A.
Sarmiento, Orlando
Oliveira, Paulo Roberto
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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.
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Bibliographic citation
Papa, E. A., Sarmiento, O., & Oliveira, P. R. (2021). An inexact proximal decomposition method for variational inequalities with separable structure. RAIRO-Operation Research, 55(2021), 873-S884. https://doi.org/10.1051/ro/2020018
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