A New Approach for Proximal Split Minimization Problems

Abdellatif Moudafi () and André Weng-Law
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Abdellatif Moudafi: Laboratoire d’Informatique et Systèmes (LIS UMR 7020 CNRS/AMU/UTLN), Aix-Marseille Université, 13288 Marseille, France
André Weng-Law: Laboratoire MEMIAD, Université des Antilles, Campus de Schoelcher, 97233 Schoelcher, Cedex, France

Mathematics, 2025, vol. 13, issue 1, 1-10

Abstract: 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.

Keywords: proximal split minimization problem; Moreau envelope; infimal post-composition; forward–backward method; Douglas–Rachford algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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