In a similar spirit of the extension of the proximal point method developed by Alves et al. [2], we propose in this work an Inertial-Relaxed primal-dual splitting method to address the problem of decomposing the minimization of the sum of three convex functions, one of them being smooth, and considering a general coupling subspace. A unified setting is formalized and applied to different average maps whose corresponding fixed points are related to the solutions of the inclusion problem associated with our extended model. An interesting feature of the resulting algorithms we have designed is that they present two distinct versions with a Gauss–Seidel or a Jacobi flavor, extending in that sense former proximal ADMM methods, both including inertial and relaxation parameters. Finally we show computational experiments on a class of the fused LASSO instances of medium size.

Revised:

Accepted:

Published online:

^{1}; Philippe Mahey

^{2}; Eladio Ocaña

^{1}

@article{OJMO_2023__4__A3_0, author = {Ernesto Or\'e and Philippe Mahey and Eladio Oca\~na}, title = {Inertial-relaxed splitting for composite monotone inclusions}, journal = {Open Journal of Mathematical Optimization}, eid = {3}, publisher = {Universit\'e de Montpellier}, volume = {4}, year = {2023}, doi = {10.5802/ojmo.22}, language = {en}, url = {https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.22/} }

TY - JOUR AU - Ernesto Oré AU - Philippe Mahey AU - Eladio Ocaña TI - Inertial-relaxed splitting for composite monotone inclusions JO - Open Journal of Mathematical Optimization PY - 2023 VL - 4 PB - Université de Montpellier UR - https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.22/ UR - https://doi.org/10.5802/ojmo.22 DO - 10.5802/ojmo.22 LA - en ID - OJMO_2023__4__A3_0 ER -

%0 Journal Article %A Ernesto Oré %A Philippe Mahey %A Eladio Ocaña %T Inertial-relaxed splitting for composite monotone inclusions %J Open Journal of Mathematical Optimization %D 2023 %V 4 %I Université de Montpellier %U https://doi.org/10.5802/ojmo.22 %R 10.5802/ojmo.22 %G en %F OJMO_2023__4__A3_0

Ernesto Oré; Philippe Mahey; Eladio Ocaña. Inertial-relaxed splitting for composite monotone inclusions. Open Journal of Mathematical Optimization, Volume 4 (2023), article no. 3, 20 p. doi : 10.5802/ojmo.22. https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.22/

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