Convergence Rate Analysis of the Majorize-Minimize Subspace Algorithm

Emilie Chouzenoux (1, 2) , Jean-Christophe Pesquet (1, 2)

1 GALEN - Organ Modeling through Extraction, Representation and Understanding of Medical Image Content
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

State-of-the-art methods for solving smooth optimization problems are nonlinear conjugate gradient, low memory BFGS, and majorize-minimize (MM) subspace algorithms. The MM subspace algorithm that has been introduced more recently has shown good practical performance when compared with other methods on various optimization problems arising in signal and image processing. However, to the best of our knowledge, no general result exists concerning the theoretical convergence rate of the MM subspace algorithm. This paper aims at deriving such convergence rates both for batch and online versions of the and in particular, discusses the influence of the choice of the subspace.

Domaines: Traitement du signal et de l'image [eess.SP]

Emilie Chouzenoux, Jean-Christophe Pesquet. Convergence Rate Analysis of the Majorize-Minimize Subspace Algorithm. IEEE Signal Processing Letters, 2016, 23 (9), pp.1284 - 1288. ⟨10.1109/LSP.2016.2593589⟩. ⟨hal-01373641⟩