Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Operator splitting
  • projective splitting
  • inertial algorithms
  • relative error
  • monotone operators

Mathematics Subject Classification

47H05, 49M27, 47N10

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Suggested citation

M. Marques Alves, M. Geremia, R. T. Marcavillaca. “A Relative-Error Inertial-Relaxed Inexact Projective Splitting Algorithm.” Journal of Convex Analysis 31 (2024), No. 1, 1–24. https://doi.org/10.68381/jca31001

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.