Open Journal of Mathematical Optimization

Inertial-relaxed splitting for composite monotone inclusions
Ernesto Oré1; Philippe Mahey2; Eladio Ocaña1
1 IMCA, Instituto de Matemática y Ciencias Afines, Universidad Nacional de Ingeniería, Lima, Perú
2 LIMOS, CNRS, Université Clermont Auvergne, France
Open Journal of Mathematical Optimization, Volume 4 (2023), article no. 3, 20 p.

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.

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Accepted:
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DOI: 10.5802/ojmo.22
Keywords: Operator splitting methods, Convex composite optimization
Ernesto Oré 1; Philippe Mahey 2; Eladio Ocaña 1

1 IMCA, Instituto de Matemática y Ciencias Afines, Universidad Nacional de Ingeniería, Lima, Perú
2 LIMOS, CNRS, Université Clermont Auvergne, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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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