Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S873 - S884|
|Published online||02 March 2021|
An inexact proximal decomposition method for variational inequalities with separable structure
Universidad Nacional del Callao, Callao, Perú
2 Universidad Privada del Norte, Trujillo, Perú
3 Systems Engineering and Computer Science Program, COPPE, Federal University of Rio de Janeiro, CP 68511, Rio de Janeiro, RJ 21941-972, Brazil
* Corresponding author: firstname.lastname@example.org
Accepted: 19 February 2020
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.
Mathematics Subject Classification: 90C33
Key words: Variational inequalities / maximal monotone operators / separable structure / proximal distances
© EDP Sciences, ROADEF, SMAI 2021
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