Inertial-relaxed splitting for composite monotone inclusions
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 conside...
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| Format: | Article |
| Language: | English |
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Université de Montpellier
2023-02-01
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| Series: | Open Journal of Mathematical Optimization |
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| Online Access: | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.22/ |
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| author | Oré, Ernesto Mahey, Philippe Ocaña, Eladio |
| author_facet | Oré, Ernesto Mahey, Philippe Ocaña, Eladio |
| author_sort | Oré, Ernesto |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ff8d900debed49bcbb2d1b1ad24d5e61 |
| institution | Kabale University |
| issn | 2777-5860 |
| language | English |
| publishDate | 2023-02-01 |
| publisher | Université de Montpellier |
| record_format | Article |
| series | Open Journal of Mathematical Optimization |
| spelling | doaj-art-ff8d900debed49bcbb2d1b1ad24d5e612025-02-07T14:02:56ZengUniversité de MontpellierOpen Journal of Mathematical Optimization2777-58602023-02-01412010.5802/ojmo.2210.5802/ojmo.22Inertial-relaxed splitting for composite monotone inclusionsOré, Ernesto0Mahey, Philippe1Ocaña, Eladio2IMCA, Instituto de Matemática y Ciencias Afines, Universidad Nacional de Ingeniería, Lima, PerúLIMOS, CNRS, Université Clermont Auvergne, FranceIMCA, Instituto de Matemática y Ciencias Afines, Universidad Nacional de Ingeniería, Lima, PerúIn 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.https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.22/Operator splitting methodsConvex composite optimization |
| spellingShingle | Oré, Ernesto Mahey, Philippe Ocaña, Eladio Inertial-relaxed splitting for composite monotone inclusions Open Journal of Mathematical Optimization Operator splitting methods Convex composite optimization |
| title | Inertial-relaxed splitting for composite monotone inclusions |
| title_full | Inertial-relaxed splitting for composite monotone inclusions |
| title_fullStr | Inertial-relaxed splitting for composite monotone inclusions |
| title_full_unstemmed | Inertial-relaxed splitting for composite monotone inclusions |
| title_short | Inertial-relaxed splitting for composite monotone inclusions |
| title_sort | inertial relaxed splitting for composite monotone inclusions |
| topic | Operator splitting methods Convex composite optimization |
| url | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.22/ |
| work_keys_str_mv | AT oreernesto inertialrelaxedsplittingforcompositemonotoneinclusions AT maheyphilippe inertialrelaxedsplittingforcompositemonotoneinclusions AT ocanaeladio inertialrelaxedsplittingforcompositemonotoneinclusions |