Journal of Convex Analysis 31 (2024), No. 1, 001--024
Copyright Heldermann Verlag 2024
A Relative-Error Inertial-Relaxed Inexact Projective Splitting Algorithm
Maicon Marques Alves
Dep. de Matemática, Universidade Federal de Santa Catarina, Florianópolis, Brazil
maicon.alves@ufsc.br
Marina Geremia
(1) Dep. de Matemática, Universidade Federal de Santa Catarina, Florianópolis, Brazil
(2) Dep. Ensino, Pesquisa e Extensão, Inst. Fed. de Santa Catarina, Florianópolis, Brazil
marina.geremia@ifsc.edu.br
Raul T. Marcavillaca
Dep. de Matemáticas, Universidad de Tarapacá, Arica, Chile
raultm.rt@gmail.com
For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits from a combination of inertial and relaxation effects, which are both controlled by parameters within a certain range. We propose sufficient conditions on these parameters and study the interplay between them in order to guarantee weak convergence of sequences generated by our algorithm. Additionally, the proposed algorithm also benefits from inexact subproblem solution within a relative-error criterion. Illustrative numerical experiments on LASSO problems indicate some improvement when compared with previous (noninertial and exact) versions of projective splitting.
Keywords: Operator splitting, projective splitting, inertial algorithms, relative error, monotone operators.
MSC: 47H05, 49M27, 47N10.
[ Fulltext-pdf (276 KB)] for subscribers only.