A New Approach for Proximal Split Minimization Problems
We provide an alternative formulation of proximal split minimization problems, a very recently developed and appealing strategy that relies on an infimal post-composition approach. Then, forward–backward and Douglas–Rachford splitting algorithms will guide both the design and analysis of some split...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/144 |
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| author | Abdellatif Moudafi André Weng-Law |
| author_facet | Abdellatif Moudafi André Weng-Law |
| author_sort | Abdellatif Moudafi |
| collection | DOAJ |
| description | We provide an alternative formulation of proximal split minimization problems, a very recently developed and appealing strategy that relies on an infimal post-composition approach. Then, forward–backward and Douglas–Rachford splitting algorithms will guide both the design and analysis of some split numerical methods. We provide evidence of globally weak convergence and the fact that these algorithms can be equipped with relaxed and/or inertial steps, leading to improved convergence guarantees. |
| format | Article |
| id | doaj-art-98bbef01ba3a4bf6857ae9e4d7c32ed6 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-98bbef01ba3a4bf6857ae9e4d7c32ed62025-01-10T13:18:24ZengMDPI AGMathematics2227-73902025-01-0113114410.3390/math13010144A New Approach for Proximal Split Minimization ProblemsAbdellatif Moudafi0André Weng-Law1Laboratoire d’Informatique et Systèmes (LIS UMR 7020 CNRS/AMU/UTLN), Aix-Marseille Université, 13288 Marseille, FranceLaboratoire MEMIAD, Université des Antilles, Campus de Schoelcher, 97233 Schoelcher, Cedex, FranceWe provide an alternative formulation of proximal split minimization problems, a very recently developed and appealing strategy that relies on an infimal post-composition approach. Then, forward–backward and Douglas–Rachford splitting algorithms will guide both the design and analysis of some split numerical methods. We provide evidence of globally weak convergence and the fact that these algorithms can be equipped with relaxed and/or inertial steps, leading to improved convergence guarantees.https://www.mdpi.com/2227-7390/13/1/144proximal split minimization problemMoreau envelopeinfimal post-compositionforward–backward methodDouglas–Rachford algorithm |
| spellingShingle | Abdellatif Moudafi André Weng-Law A New Approach for Proximal Split Minimization Problems Mathematics proximal split minimization problem Moreau envelope infimal post-composition forward–backward method Douglas–Rachford algorithm |
| title | A New Approach for Proximal Split Minimization Problems |
| title_full | A New Approach for Proximal Split Minimization Problems |
| title_fullStr | A New Approach for Proximal Split Minimization Problems |
| title_full_unstemmed | A New Approach for Proximal Split Minimization Problems |
| title_short | A New Approach for Proximal Split Minimization Problems |
| title_sort | new approach for proximal split minimization problems |
| topic | proximal split minimization problem Moreau envelope infimal post-composition forward–backward method Douglas–Rachford algorithm |
| url | https://www.mdpi.com/2227-7390/13/1/144 |
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